Question

If the radius of a right circular cylinder open at both the ends is decreased by $25\%$ and the height of the cylinder is increased by $25\%$, then the surface area of the cylinder thus formed is:

• A. Remains unaltered
• B. Increases by $25\%$
• C. Decreases by $25\%$
• D. Decreases by $6.25\%$

Answer 1

The correct option is D Decreases by $6.25\%$

Let the radius of the original cylinder $=r$ cm and height $=h$ cm
Surface Area of a Cylinder $=2\pi rh$

New radius after decrease $=\frac{75r}{100}=0.75r$
New height after increase $=\frac{125}{100}h=1.2h5$
New surface area of the cylinder $=2\pi \times 0.75r\times 1.25h=1.875\pi rh$
Since, $1.875<2$, the surface area has decreased.
%decrease $=\frac{\text{Original Surface area - New Surface Area}}{\text{Original Surface Area}}\times 100$

$=\frac{2\pi rh-1.875\pi rh}{2\pi rh}\times 100$

$=\frac{0.125}{2}\times 100=6.25\%$