Intro: Circle Study Guide - District 95

Intro: Circle Study Guide

Find the circumference of the circle. Use π ≈ 3.14.
____ 1.

7 cm

a. 21.98 cm b. 38 cm c. 7 cm d. 3.5 cm
____ 2.

3m

a. 3 m b. 18.84 m c. 6 m d. 28.26 m

Find the circumference of the circle with the given radius or diameter. Use π ≈ 3.14.

____ 3. radius = 30 cm b. 94.2 cm c. 2,826 cm d. 11,304 cm
a. 188.4 cm

____ 4. diameter = 10 cm b. 78.5 cm c. 314 cm d. 15.7 cm
a. 31.4 cm

____ 5. Kelsey’s dog Spot has an exercise area behind the house. A stake in the ground has a 15-foot rope tied to it.

The other end of the rope is fastened to Spot’s collar. If Spot travels in a circular path around the stake, what

is the largest circumference allowed by the rope’s length? Round your answer to the nearest foot.

a. 94 feet b. 177 feet c. 47 feet d. 24 feet

Students on a field trip at an amusement park were asked their grade in school. The table shows the
results of the survey.

Grade Number of Students
4th 45
5th 25
6th 60
7th 50
8th 60
9th 45

____ 6. What percent of the students surveyed were in 9th grade? Round your answer to the nearest percent, if

necessary.

a. 45% b. 9% c. 8% d. 16%

____ 7. Suppose you want to show the data in a circle graph. Find the measure of the central angle for 5th grade.

Round your answer to the nearest degree, if necessary.

a. 9 b. 32 c. 16 d. 25

Find the exact area of the circle.
____ 8.

3 in.

a. 9π in.2 b. 28π in.2 c. 9π in.2 d. 19π in.2

____ 9.

3 in.

a. 2.25π in.2 b. 3π in.2 c. 9π in.2 d. 1.5π in.2

____ 10. Find the area of a circle with radius 8.1 m to the nearest square unit.

a. 66 m2 b. 824 m2 c. 206 m2 d. 51 m2

____ 11. A particular model of walkie-talkie can broadcast in a circular area. The radius of the broadcast area is 10,000

feet. Find the area of this circle to the nearest square foot. Use 3.14 for π.
a. 314,000,000 ft2 c. 1,256,000,000 ft2

b. 100,000,000 ft2 d. 62,800 ft2

____ 12. The diagram shows a square of side 3 in. containing a circle of diameter 3 in. To the nearest hundredth, what
is the area of the shaded part of the figure? Use 3.14 for π.

a. 0.48 in.2 b. 1.93 in.2 c. 4.03 in.2 d. 4.82 in.2

____ 13. Find the area of the figure to the nearest square unit.

3 cm 8 cm c. 37 cm2 d. 125 cm2

a. 74 cm2 b. 49 cm2

14. At the Magic Garden, a rose garden is being designed as shown. The outer figure is a square with side length
of 116 feet.

a. What is the diameter of one circle? Explain how you find the diameter.
b. The roses are to be planted in the four circles. The rest of the space will be covered by wood chips. What is

the area of the surface that will be covered by wood chips? Explain how you find this area.

15. Given the Circumference find both the diameter and radius. Round to the nearest whole unit.

a. C= 44 in b. C= 47.1 cm c. C=301.44 cm

16. Given the Area find the radius. Round to the nearest whole unit.

a. A= 78.5 sq cm b. A= 9856 sq ft c. A= 5544 sq ft

Intro: Circle Study Guide

Answer Section

MULTIPLE CHOICE

1. ANS: A
2. ANS: B
3. ANS: A
4. ANS: A
5. ANS: A
6. ANS: D
7. ANS: B
8. ANS: C
9. ANS: A
10. ANS: C
11. ANS: A
12. ANS: A
13. ANS: B
ESSAY

14. ANS: The length of one side of the square is 116 feet. There are two circles across the
[4] a.
square, so the diameter of one circle is 116 ÷ 2 or 58 feet.
b.
To find the area of the wood chips, find the area of the square and subtract the

area of four circles.

Use the formula for the area of a square.

= 116 ⋅ 116 Substitute 116 for s.

= 13,456 Simplify.

Use the formula for the area of a circle. Multiply by 4.

4 • 3.14 ⋅ 292 Substitute 3.14 for π and 29 for the radius.

= 10,563 Simplify.

area of square – area of 4 circles = 13,456 – 10,563 or 2,893

The area of surface covered by wood chips is about 2,893 square feet.

15a) d=14 in; r= 7 in
b) d=15 cm; r= 7.5 cm
c) d= 96 cm; r= 48 cm

16a) r= 5cm
b) r= 56 ft
c) r= 42 ft