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Volume of a Cylinder

Let us take a cuboidal and a cylindrical object. On observing, we
see that there are some similarities between them. r
h
For example, just like a cuboid, a cylinder has got a pair of
congruent and parallel top and base. Also, like a cuboid, the h
lateral surface of a cylinder is perpendicular to the base.
b
Using these facts, we can find the volume of a cylinder in a l
similar manner that we have used for a cuboid.

Since, the volume of a cuboid = Area of base × height

Similarly, the volume of a cylinder = Area of base × height
Here, the base of the cylinder is a circle of radius r and h is the height of the cylinder, then

2
2
Volume of the cylinder = Area of its circular base × height = pr × h = pr h
2
Thus, the volume of a cylinder = pr h.
Example 30: Find the volume of a cylinder having a radius 10 cm and height 14 cm.
2
Solution: We have, the volume of a cylinder = pr h
Here, the radius of the cylinder = 10 cm and height of the cylinder = 14 cm 14 cm
22 10 cm
So, the volume of the cylinder = pr h = × 10 cm × 10 cm × 14 cm = 4400 cm .
3
2
7
3
Example 31: Find the height of a cylinder whose volume is 7.92 m and diameter of the base is
120 cm.
Solution: Let the diameter of the base of cylinder = 2r
120
\ 2r = 120 cm ⇒ r = cm = 60 cm.
2
Let h be the height of the cylinder.

Q Volume of the cylinder = 7.92 m 3 Think and Answer
= 7.92 × 100 × 100 × 100 cm 3 In the figure, a cylindrical water
storage tank is shown. In which situation will
[Q 1 m = 100 cm] you find the surface area, and the volume?

2
We have, volume of a cylinder = pr h
3
2
⇒ pr h = 7.92 × 100 × 100 × 100 cm
22
⇒ × ( 60 cm ) 2 × h = 7920000 cm 3
7
7920000 7 (a) To find out how much water it can hold.
×
\ h = cm
×
×
22 60 60 (b) To find the number of cement bags
required to plaster it from outside.
= 100 × 7 cm (c) To find the number of smaller tanks
= 700 cm required to fill water from it.
= 7 m.
Thus, the height of the cylinder is 7 m.

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