class 10 prism

7.2 8:22 AM

Tuesday, February 2, 2021

Prism and pyramid
6 a)
find the cross section area lateral surface area ,total surface area and volume of a
triangular prism whose sides of base area 4,13, 15 cm and length 20
solution
Solution
Sides of right angle triangle are 4,13,15 respectively
we have,

area of the base =

=
Perimeter of the triangle = 4+13+15

=32
Latera surface area =

=

Total surface area = latera surce area

7 a) The length of a prism having right angled isosceles triangular base is 100 cm
volume 12000 cubic cm find the measures of the base
solution
we have
Volume of the prism = Area of base height
12000=Area of base 100
Area of base =120

Being isosceles triangle p=b

mensuration Page 1

b=
Area of base is Right angle triangle so using Pythagoras theorem

h=
8 a) l=12
sides of right isosceles triangle are

area of triangular base=

=36
LSA of triangular prism =

=(

TSA of triangular prism =

volume of triangular prism=

9a) find the cross section area lateral surface area ,total surface area and volume of a
triangular prism having length 28 cm and measurement of right angled triangular base
sides 10 cm 8 cm and 6 cm respectively
Solution
Sides of right angle triangle are 10 ,8,6
area of the base =

Perimeter of the triangle = 10+8+6 latera surce area
=24

Latera surface area =
=

Total surface area =

mensuration Page 2

Total surface area = latera surce area

10 a) find the cross section area lateral surface area ,total surface area and volume of
a triangular prism having length 28 cm and measurement of triangular base sides 6 ,
25, and 29 cm respectively
solution
Solution
Sides of right angle triangle are 6,25,29 respectively
we have,

area of the base =

=

Perimeter of the triangle = 6+25+29
=60

Latera surface area =
=

Total surface area = latera surce area

Pyramid EX 7.2

4a) find the volume of a squared pyramid if its base is 49 m2 and height 12 cm.
solution:
area of the base (
height of pyramid ( h )=12
we have
volume of the pyramid =

=
5a) the volume of a squared base pyramid of height 6 cm is 32 cm3 find the length of
its base
height of the pyramid ( h ) = 6
Volume of the pyramid ( V ) =32

mensuration Page 3

Volume of the pyramid ( V ) =32
length of the base (a ) =?
we have
volume of the pyramid =
32=

a= 4
the lenth of side of the base is 4

6a) A pyramid having squared base has a triangular face of height 18 cm and the
length of base 1.5 cm find the total surface area
solution :
slant height ( l)=18
a=1.5
TSA of pyramid =

7a) A pyramid has square base of side 24 cm and slant height is 13 cm find the total
surface area and the volume
Solution :
Side of the base (a )=24
Slant height (h ) =13
TSA of the pyramid = ?
volume of pyramid=?
we have

TSA of pyramid =

volume of the pyramid ( V) =

8a) in the given figure the total surface are of given squared based pyramid is 96 cm2
and the side of the square base is 6 cm find the slant height of the pyramid .
solution:
TSA of the pyramid =96
Side of the base (a ) = 6 cm
slant height ( l )=?
we have,

mensuration Page 4

we have,
TSA of pyramid =
96=

Again we have,

9)The pyramid with square base of vertical height 16 cm and of slant height 20 cm is
shown in the figure calculate : volume of the pyramid latera surface area of the
pyramid total surface area of the pyramid
Solution:
height of the pyramid(h) = 16
slant height ( l) = 20
we have

volume of the pyramid ( V) =

lateral surface area of pyramid =

Total surface area of pyramid=

10 a) find the total volume
solution :
a=3

Volume of the solid= volume of upper pyramid + volume of lower pyramid
=

=
=

11) Find the TSA of the following solid
solution :
a=20

mensuration Page 5

a=20
slant height of upper pyramid(l1)=20
slant height of lower pyramid(l1)=18
TSA of solid= LAS of upper pyramid+ LSA of lower pyramid

=

12) A pyramid is made above a cuboid with measure 90 If the height of

the pyramid including cubiod is 240 cm , find the total volume

solution:
side of base of pyramid(a)=90

Height of the prism = 225
combined height =240
height of the pyramid=240-225=15
Volume of the solid= volume of the Prism + volume of pyramid

= base of pyramid on the prism so , a=l

=

13) find the total surface area of the combined solid made by the pyramid and prism
solution :
a=2.5
Let h and h1 be the height of the pyramid and prism
Height of the prism (h1 ) =7

h=3
we have ,

TSA of the solid = Area of base of prism+ Area of 4 wall of the + LSA of the Pyramid
=

14a) If the combine solid made by the pyramid and prism in the given solid is 336 2
find the height of the pyramid .
solution:
length of the prism (a)= 6
height of prism (h1)=10

length of side of the base (a)=6
slant height (l)=?
TSA of the solid = Area of base of prism+ Area of 4 wall of the + LSA of the Pyramid

336 =
336= 36+240+

mensuration Page 6

336 =
336= 36+240+
12 l=336-276

l= 5

we have ,

15 a) in the adjoining solid , a square based pyramid is situated on the top of a square
based cuboid so that the total height of the solid is 15 . If the volume of the pyramid
and cuboid are 300 and 600 respectively find the height of the pyramid
solution :

volume of cuboid=600

volume of pyramid=300

or

Dividing we get

h=
putting value in equation

Q 16 a solid consists of square based prism of height 6.5 exactly fitting of a right
pyramid of slant height 5 cm on the top . If the volume of lower part is 416 cm3 find the
height of the pyramid find the volume of the pyramid
solution:
Volume of cuboid= 416

l=8
for the pyramid
a=8 l=5

mensuration Page 7

a=8 l=5
we have
h=3
volume of pyramid =

=

mensuration Page 8