Question

Question 12

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

Let h' be the new height.
Curved surface area of a cylinder with radius r and height h
$=2\pi rh$
Now, according to the question, radius is tripled. Then,
Curved surface area $=2\pi \times 3r\times h^{\prime }=2\pi rh$
$\Rightarrow 6\pi r\times h^{\prime }=2\pi rh$ [given]
$\Rightarrow h^{\prime }=\frac{2\pi rh}{6\pi r}$
$\therefore h^{\prime }=\frac{1}{3}h$
Hence, the new height will be $\frac{1}{3}$ of the original height.