Question

The height of circular cone is 30 cm. and it is constant. The radius of the base is increasing at the rate of 0.25cm/sec. Find the rate of increase of volume of the cone when the radius of base is 10cm.

Answer 1

Given h = 30 cm, \(\frac{dr}{dt}\) = 0.25cm/sec. r = 10cm. dt 

V = \(\frac{1}{3}\)πr²h 

\(\frac{dv}{dt}\) = \(\frac{\pi}{3}\)h.2r.\(\frac{dr}{dt}\) = π. \(\frac{30}{3}\). 20.(0.25) 

= 50π cm²/sec