If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).

A.

\(\frac{\pi h}{3} (2R + r)\)

B.

\(2R + r + \frac{\pi h}{3}\)

C.

\(\frac{\pi h}{3} (2R^2 + r + 2r)\)

D.

\(\frac{2R^2}{3} \pi h\)

Correct answer is A

\(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\)

\(V = \frac{\pi R^2 h}{3} + \frac{\pi Rr h}{3} + \frac{\pi r^2 h}{3}\)

\(\frac{\mathrm d V}{\mathrm d R} = \frac{2 \pi R h}{3} + \frac{\pi r h}{3}\)

= \(\frac{\pi}{3} (2R + r)\)