Question

Radius of cylinder is r and height is h fund the change in volume if a- height is doubled b- height is duloulbled and radius is halfed

Answer 1

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The curved surface area of a cylinder =2πrh2πrh

If radius (r) is doubled and height (h) is halved

The curved surface area of a cylinder

=2π×2r×h22π×2r×h2

Hence the curved surface area of the cylinder does not change. 

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Answer 2

a. the initial volume of the cylinder is
V = πr^2h.
the volume after h is doubled is
V = πr^22h
the change in volume will be

final - initial volume
πr^22h-πr^2h = πr^2h.

b.if height is doubled and radius is halved then

V = π(1/4)r^22h.
change in volume = π(1/2)r^2h-πr^2h = -πr^2h

HERE the minus sign over the volume indicates that volume is decreased.

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