Question

Question 6

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) Curved surface area of the cylinder will be doubled
(b) Curved surface area of the cylinder will remain unchanged
(c) Curved surface area of the cylinder will be halved
(d) Curved surface area will be $\frac{1}{4}$ of the original curved surface

Answer 1

Let the new height and radius be $\frac{h}{4}$ and 2r respectively, where r and h are orignal radius and original height respectively of the cylinder.
We know that, curved surface area of cylinder $=2\pi rh$
$=2\pi \left(2r\right)\times \frac{1}{4}h=4\pi r\times \frac{1}{4}h=\pi rh$
$=\frac{1}{2}\times 2\pi rh$ [multiplying and dividing by 2]
$=\frac{1}{2}$ original curved surface area
Hence, the curved surface area of the cylinder will be halved.