Question

The radius of a sphere is given by $r=2t$. The rate of change of surface area at $t=1$ is equal to

• A. $8\pi$
• B. $32\pi$
• C. $16\pi$
• D. $4\pi$

Answer 1

Answer: (B)

$32\pi$

Given $r=2t$

$s=4\pi r^2=4\pi \times 4t^2$

=$16\pi t^2$

$\frac{ds}{dt}=32\pi t$

at $t=1$

$\frac{ds}{dt}=32\pi$