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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(V = \frac{2}{3} \pi r^{3}\)
\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\)
\(\frac{\mathrm d V}{\mathrm d r} (r = 2) = 2\pi (2)^{2}\)
= \(8\pi\)
Source: Myschool Past Questions Archive (Record #8049)