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A day full of math games & activities. Find one near you.

Radius of a cylinder is r and the height is h. Find the change in the volume if the
(a) height is doubled.
(b) height is doubled and the radius is halved.
(c) height remains same and the radius is halved.

Solution:

Volume of a cylinder of radius r and height h is given by:

Volume = πr²h

(a)If the height is doubled the new Volume will be V’ given by

V’ = 2πr²h

And the ratio of new volume to old volume will be

V’/V = 2πr²h/πr²h = 2:1

Therefore the volume will be doubled.

(b) If the height is doubled and the radius halved the new Volume is:”

V’ = π(r/2)²2h = 1/2 × πr²h

Therefore the ratio of the new volume to old volume will be

V’/V =[ 1/2 × πr²h]/[πr²h ] = 1:2

The new volume will become half of the original volume.

(c) If the radius is halved keeping the height same

V’ = π(r/2)²h = 1/4 × πr²h

Therefore the ratio of the new volume to old volume will be

V’/V = [1/4 × πr²h]/πr²h = 1/4

The new volume will be one fourth of the original volume

✦ Try This: Radius of a cylinder is r and the height is h. Find the change in the volume if the

(a) height is tripled.

(b) height remains same and the radius is doubled

(c) height is reduced to one-fourth and the radius is doubled.

Volume of a cylinder of radius r and height h is given by:

Volume = πr²h

(a)If the height is tripled the new Volume will be V’ given by

V’ = πr²(3h)

V’ = 3πr²h

And the ratio of new volume to old volume will be

V’/V = 3πr²h/πr²h = 3:1

Therefore the volume will be tripled

(b) If the height remains same and the radius is doubled then the new Volume V’ becomes

V’ = π(2r/)²h = 4πr²h

Therefore the ratio of the new volume to old volume will be

V’/V = [4πr²h]/[πr²h ] = 4:1

The new volume will become four times the original volume.

(c) If the height is reduced to one-fourth of the original heigh and the radius is doubled

V’ = π(2r)²(h/4) = 4πr²(h/4) = πr²h

Therefore the ratio of the new volume to old volume will be

V’/V = [πr²h]/πr²h = 1

The new volume will be the same as the original volume.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 92

Radius of a cylinder is r and the height is h. Find the change in the volume if the (a) height is doubled, (b) height is doubled and the radius is halved, (c) height remains same and the radius is halved.

Summary:

Radius of a cylinder is r and the height is h. The change in the volume if the (a) height is doubled the ratio of the new volume will be twice, (b) height is doubled and the radius is halved, (c) height remains same and the radius is halved

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