Question

If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be.
(a) tripled
(b) constant
(c) one sixth
(d) one third​

Answer 1

Curved surface area of a cylinder = 2πrh

radius = r

height = h

if radius is the tripled,

radius = 3r

height = ? let us take height as x

curved surface area = 2πrh

hence,

$2\pi \times 3rx = 2\pi \times rh$

$\frac{2\pi}{2\pi} \times 3rx = rh$

$1 \times 3rx = rh$

$3rx = rh$

$x = \frac{rh}{3r}$

$x = \frac{h}{3}$

hence option (d) is correct.

The height will be one third of what it initially was.

hope it helps

have a great day