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If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true?
(a) Volume of the cylinder will be doubled.
(b) Volume of the cylinder will remain unchanged.
(c) Volume of the cylinder will be halved.
(d) Volume of the cylinder will be 1/4 of the original volume

Solution:

If the height of the cylinder is h and the radius is r then the volume of the cylinder is given as:

Volume (V) = πr²h

If the height is now changed from h to h/4 and the radius is doubled to 2r then the new volume will be

Volume (V’) = π(2r)²(h/4)

V = 4πr²(h/4)

V = πr²h

Hence the Volume Remains Unchanged.

The correct answer is (b)

✦ Try This: If the height of a cylinder becomes 1/2 of the original height and the radius remains same, then which of the following will be true?

(a) Volume of the cylinder will be doubled.

(b) Volume of the cylinder will remain unchanged.

(c) Volume of the cylinder will be halved.

(d) Volume of the cylinder will be 1/4 of the original volume.

Solution:

If the height of the cylinder is h and the radius is r then the volume of the cylinder is given as:

Volume (V) = πr²h

If the height is now changed from h to h/2 and the radius remains same as r then the new volume will be

Volume (V’) = π(r)²(h/2)

V = (1/2)πr²(h)

V = (1/2)πr²h

Hence the Volume will be halved.

The correct answer is c

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 5

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true? (a) Volume of the cylinder will be doubled (b) Volume of the cylinder will remain unchanged (c) Volume of the cylinder will be halved (d) Volume of the cylinder will be 1/4 of the original volume

Summary:

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then the volume of the cylinder will remain unchanged

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