What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
-
A.
8π -
B.
16π -
C.
2π -
D.
4π
Correct Answer: Option A
Explanation
(V = frac{2}{3} pi r^{3})
(frac{mathrm d V}{mathrm d r} = 2pi r^{2})
(frac{mathrm d V}{mathrm d r} (r = 2) = 2pi (2)^{2})
= (8pi)