Question

If the volume of a sphere increases by 72.8%, then its surface area increases by

• A. 20%
• B. 44%
• C. 24.3%
• D. 48.6%

Answer 1

The correct option is B 44%

$\frac{V^{\prime }}{V}=\frac{172.8}{100}=\frac{\frac{4}{3}\pi R^{.3}}{\frac{4}{3}\pi R^3}$
$\frac{R^{\prime }}{R}=1.2$
Now, ratio of surface area $=\frac{S^{\prime }}{S}=\frac{4\pi R^{.2}}{4\pi R^3}$
$=\frac{S^{\prime }}{S}=1.44$
Hence surface area increased by 44%