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: Option A
Explanation
(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))
There is an explanation video available below.