What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
-
8Ο
- 16Ο
- 2Ο
- 4Ο
The correct answer is: A
Explanation
\(V = \frac{2}{3} \pi r^{3}\)
\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\)
\(\frac{\mathrm d V}{\mathrm d r} (r = 2) = 2\pi (2)^{2}\)
= \(8\pi\)