พื้นที่ผิวและปริมาตร ปริมาตร ปริมาตรของทรงสี่เหลี่ยมมุมฉาก หาได้จากสูตร ปริมาตรของทรงสี่เหลี่ยมมุมฉาก = พื้นที่ฐาน x ความสูง ตัวอย่างที่ 1 หาปริมาตรของทรงสี่เหลี่ยมมุมฉากต่อไปนี้ .................................................................................................................................. . .................................................................................................................................. . .................................................................................................................................. . .................................................................................................................................. . ตัวอย่างที่ 2 มาโนชต้องการขุดสระน ้าทรงสี่เหลี่ยมมุมฉากที่มีขนาดกว้าง 20 เมตร ยาว 35 เมตร ลึก 1.7 เมตร มาโนชจะขุด ดินได้กี่ลูกบาศก์เมตร .................................................................................................................................. ....................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ตัวอย่างที่ 3 หาปริมาตรของทรงสี่เหลี่ยมมุมฉากต่อไปนี้ .................................................................................................................................. . .................................................................................................................................. . .................................................................................................................................. . แบบฝึกทักษะ หาปริมาตรของทรงสี่เหลี่ยมมุมฉากต่อไปนี้ 1. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... 2. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ...............................................................................................................
3. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... 4. ................................................................................................ ................................................................................................. ................................................................................................. ................................................................................................. 5. บ่อน ้าแห่งหนึ่งกว้าง 25 เมตร ยาว 50 เมตร ลึก 8 เมตร มีน ้าอยู่ในบ่อวัดปริมาตรได้ 8,750 ลูกบาศก์เมตร อยากทราบว่าผิว น ้าอยู่ลึกจากปากบ่อเท่าไร .................................................................................................................................. ....................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ........................................................................................................................................................ ................................................. ......................................................................................................................................................................... ................................ 6. แท็งก์น ้าทรงสี่เหลี่ยมมุมฉากมีความกว้าง 3 ฟุต ความยาว 4 ฟุต และความสูง 5 ฟุต แท็งก์น ้านี้จุน ้าได้กี่แกลลอน (1 ลูกบาศก์ฟุต = 7.5 แกลลอน) .................................................................................................................................. ....................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ........................................................................................................................................................ ................................................. พื้นที่ผิวและปริมาตรของปริซึม พื้นที่ผิวของปริซึม หาได้จากสูตร พื้นที่ผิวของปริซึม = พื้นที่ฐานทั้งสอง + พื้นที่ผิวข้าง ปริซึมตรงจะมีผิวข้างตั้งฉากกับฐาน แต่ถ้าปริซึมเอียงผิวข้างจะไม่ตั้งฉากกับฐาน
การเรียกชื่อปริซึมจะเรียกตามลักษณะของฐานหรือหน้าตัด ตัวอย่างที่ 1 หาพื้นที่ผิวของปริซึม .............................................................................................................................. .. ................................................................................................................................ ................................................................................................................................ ................................................................................................................................ ตัวอย่างที่ 2 หาพื้นที่ผิวของปริซึม ................................................................................................................................ ................................................................................................................................ ................................................................................................................................ ................................................................................................................................ ................................................................................................................................ ................................................................................................................................ ตัวอย่างที่ 3 พื้นที่ผิวของปริซึมเป็น 448 ตารางเซนติเมตร ฐานของปริซึมเป็นรูปสี่เหลี่ยมจัตุรัสยาวด้านละ 8 เซนติเมตร ความ สูงของปริซึมเป็นเท่าไร ................................................................................................................................. ........................................................................ ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ....................................................................................................................................................... ..................................................
แบบฝึกทักษะ 1. หาพื้นที่ผิวของปริซึมต่อไปนี้ .................................................................................................................. .................................................................................................................. ................................................................................................................... ................................................................................................................... .................................................................................................................. ................................................................................................................... ................................................................................................................... ................................................................................................................... .................................................................................................................. ................................................................................................................... ................................................................................................................... ................................................................................................................... .................................................................................................................. ................................................................................................................... ................................................................................................................... ................................................................................................................... 2. เส้นรอบรูปของฐานปริซึมสี่เหลี่ยมจัตุรัสยาว 72 เซนติเมตร ความสูงของปริซึมเป็น 5 เมตร พื้นที่ผิวข้างเป็นเท่าไร .................................................................................................................................. ....................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ปริมาตรของปริซึม หาได้จากสูตร ปริมาตรของทรงปริซึม = พื้นที่ฐาน x ความสูง ตัวอย่างที่ 1 ปริซึมสี่เหลี่ยมผืนผ้ามีความกว้าง 3 หน่วย ความยาว 4 หน่วยความสูง 7 หน่วยหาปริมาตรของปริซึมสี่เหลี่ยมนี้ .................................................................................................................................. ....................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... .........................................................................................................................................................................................................
ตัวอย่างที่ 2 ปริซึมสามเหลี่ยมมีปริมาตร 60 ลูกบาศก์เซนติเมตร ความสูง 5 เซนติเมตร พื้นที่ท่านเป็นเท่าไร .................................................................................................................................. ....................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ตัวอย่างที่ 3 ปริซึมสี่เหลี่ยมจัตุรัสกว้างด้านละ 9 เซนติเมตร มีปริมาตร 1,215 ลูกบาศก์เซนติเมตร ความสูงของปริซึมเป็นเท่าไร .................................................................................................................................. ....................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... แบบฝึกทักษะ 1. หาปริมาตรของปริซึมต่อไปนี้ .................................................................................................................. ................................................................................................................... ................................................................................................................... .................................................................................................................. ................................................................................................................... ................................................................................................................... ................................................................................................................... .................................................................................................................. ................................................................................................................... ................................................................................................................... ................................................................................................................... .................................................................................................................. ................................................................................................................... ................................................................................................................... ................................................................................................................... ................................................................................................................... ...................................................................................................................
2. หาปริมาตรของปริซึมซึ่งมีพื้นที่ฐานเป็น 80 ตารางเซนติเมตร ความสูงเป็น 18 เซนติเมตร .............................................................................................................................................................................. .................................................................................................................................. ....................................................................... ................................................................................................................................................... .............................................................................................................................................................................. 3. ปีบบรรจุน ้าตาลทรงสี่เหลี่ยมมุมฉาก ก้นถังเป็นรูปสี่เหลี่ยมจัตุรัสยาวด้านละ 13 เซนติเมตร สูง 25 เซนติเมตร จะบรรจุ น ้าตาลได้กี่ลูกบาศก์เซนติเมตร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... พื้นที่ผิวและปริมาตรของปริซึม พื้นที่ผิวของทรงกระบอก หาได้จากสูตร พื้นที่ผิวของทรงกระบอก = 2 2 r 2 rh + เมื่อ r แทนรัศมีของฐานของทรงกระบอก h แทนความสูงของทรงกระบอก ตัวอย่างที่ 1 กระป๋องออมสินทรงกระบอกใบหนึ่งสูง 10 เซนติเมตร เส้นผ่านศูนย์กลางของฐานยาว 49 เซนติเมตร ต้องการปิด กระดาษรอบข้างของกระป๋อง จะต้องใช้กระดาษอย่างน้อยเท่าไร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ตัวอย่างที่ 2 หาพื้นที่ฐานของทรงกระบอกตันซึ่งมีเส้นผ่านศูนย์กลางของฐานยาว 14 เซนติเมตร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... .........................................................................................................................................................................................................
ตัวอย่างที่ 3 หาพื้นที่ผิวของทรงกระบอกตัน รัศมียาว 21 เซนติเมตร สูง 13 เซนติเมตร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... แบบฝึกทักษะ หาพื้นที่ผิวของทรงกระบอกต่อไปนี้(กำหนดให้ 3 14. ) 1. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. 2. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. 3. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. 4. ทรงกระบอกสูง 20 เซนติเมตร รัศมียาว 3.5 เซนติเมตร พื้นที่ผิวของทรงกระบอกเป็นเท่าไร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 5. ทรงกระบอกสูง 9 เซนติเมตร เส้นผ่านศูนย์กลางของฐานยาว 12 เซนติเมตร พื้นที่ผิวข้างของทรงกระบอกเป็นเท่าไร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... .........................................................................................................................................................................................................
ปริมาตรของทรงกระบอก หาได้จากสูตร ปริมาตรของทรงกระบอก = 2 r h เมื่อ r แทนรัศมีของฐานของทรงกระบอก h แทนความสูงของทรงกระบอก ตัวอย่างที่ 1 เหยือกน้ำทรงกระบอกวัดเส้นผ่านศูนย์กลางของฐานภายในได้ 14 เซนติเมตร วัดส่วนสูงได้ 15 เซนติเมตร เหยือก น้ำใบนี้จุน้ำได้เท่าไร (กำหนดให้ 22 7 = ) ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... ตัวอย่างที่ 2 ถ้าทรงกระบอกมีปริมาตรประมาณ 39,250 ลูกบาศก์เซนติเมตร มีเส้นผ่านศูนย์กลางยาว 50เซนติเมตร ถัง ทรงกระบอกมีความสูงเท่าไร (กำหนดให้ 3 14. ) ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... แบบฝึกทักษะ หาปริมาตรของทรงกระบอกต่อไปนี้(กำหนดให้ 3 14. ) 1. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. 2. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. 3. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... ..
4. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. 5. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. .................................................................................................................... .. 6. แท่งแก้วตันทรงกระบอกวัดโดยรอบแท่งแก้วได้ 132 นิ้ว มีความยาว 96 นิ้ว แท่งแก้วนี้มีปริมาตรเท่าไร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... ......................................................................................................................................................................................................... 7. แก้วน้ำทรงกระบอกใบหนึ่งวัดเส้นผ่านศูนย์กลางภายในได้ 8 เซนติเมตร มีความลึก 12 เซนติเมตร แก้วน้ำใบนี้จุน้ำได้เท่าไร ......................................................................................................................................................................................................... ....................................................................................................... .................................................................................................. ......................................................................................................................................................................................................... .........................................................................................................................................................................................................