Question

If the diameter of a sphere is decreased by $25\%$, by what percent does its curved surface area decrease?

• A. $43.75\%$
• B. $21.88\%$
• C. $50\%$
• D. $25\%$

Answer 1

The correct option is A $43.75\%$

Curved surface area of sphere$=4\pi r^2$
diametre after decreases by $25\%$
$A_D=\pi d^2$
$d_1=\frac{75}{100}d=\frac{3d}{4}$
$A_1=\pi {\left(\frac{3d}{4}\right)}^2=\frac{9}{16}\pi d^2$
$\%$ decrease=$\frac{\frac{9}{16}\pi d^2-\pi d^2}{\pi d^2}\times 100=-43.75\%$