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If the height of a cylinder becomes 1/4th of the original height and the radius is doubled, then which of the following will be true?
(a) Total surface area of the cylinder will be doubled.
(b) Total surface area of the cylinder will remain unchanged.
(c) Total surface of the cylinder will be halved.
(d) None of the above

Solution:

The total surface area of a cylinder(SA) = 2πrl + 2πr² = 2πr(r + l)

r = radius of the cylinder

l = length or height of the cylinder

If the height of the cylinder is reduced to 1/4th of the original height and radius is doubled then,

l’ = l/4 and r’ = 2r

SA’ = 2πr’(r’ + l’)

SA’ = 2π(2r)(2r + l/4)

SA’ = 4πr(2r + l/4)

SA’ = 8πr(r + l/8)

Hence The correct answer is (d) i.e. None of the above.

✦ Try This: If the height of a cylinder becomes half of the original height and the radius is is also halved, then which of the following will be true?

(a) Total surface area of the cylinder will be doubled.

(b) Total surface area of the cylinder will remain unchanged.

(c) Total surface of the cylinder will be halved.

(d) None of the above.

The total surface area of a cylinder(SA) = 2πrl + 2πr² = 2πr(r + l)

r = radius of the cylinder

l = length or height of the cylinder

If the height of the cylinder is reduced to half of the original height and radius is halved then,

l’ = l/2 and r’ = r/2

SA’ = 2πr’(r’ + l’)

SA’ = 2π(r/2)(r/2 + l/2)

SA’ = (1/2)πr(r + l)

SA’ = (1/2)SA

Hence The correct answer is (c) i.e. total surface area will be halved.

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 7

If the height of a cylinder becomes 1/4th of the original height and the radius is doubled, then which of the following will be true? (a) Total surface area of the cylinder will be doubled (b) Total surface area of the cylinder will remain unchanged (c) Total surface of the cylinder will be halved (d) None of the above

Summary:

If the height of a cylinder becomes 1/4th of the original height and the radius is doubled, then the answer is none of the above

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