Question

If the height of a cylinder becomes $\frac{1}{4}$ 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 area of the cylinder will be halved
(d) None of the above

Answer 1

We know that,
Total surface area of cylinder having radius $r$ and height $h=2\pi r(h+r)$
Total surface area of the cylinder with new height $\left(\frac{h}{4}\right)$ and radius $2r$
$=2\pi \left(2r\right)(2r+\frac{1}{4}h)$
$=4\pi r(8r+h)\times \frac{1}{4}$
$=\pi r(8r+h)$ is can't be written multiple of $2\pi r(h+r)$.
Thus, the total surface area of new cylinder can't be multiple of total surface area of original cylinder.
Hence, the correct option is (d) (None of the above)