Question

The surface area of a sphere when its volume is increasing at the same rate as its radius is

• A. $1$
• B. $\frac{1}{2\sqrt{\pi }}$
• C. $4\pi$
• D. $\frac{4\pi }{3}$

Answer 1

The correct option is A $1$

Volume of sphere $V=\frac{4}{3}\pi r^3$

$\Rightarrow \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

$\Rightarrow (1-4\pi r^2)\frac{dr}{dt}=0$

$\Rightarrow r^2=\frac{1}{4\pi }$

Now, surface area of sphere $S=4\pi r^2$

$\Rightarrow S=1sq.unit$