Question

I found this question in the Sample Assessment Material of the iGCSE Further Pure Maths.

The volume of a right circular cone is increasing at the rate of 45 cm3 s–1. The height of the cone is always three times the radius of the base of the cone. Find the rate of increase of the radius of the base, in cms–1, when the radius of the cone is 4 cm. Give your answer correct to 3 significant figures.

Answer 1

Hello,

Thinking further,

V(R,h)=f(R) for h=3R

V=πR²*3R/2=πR^3


dV/dt=45
but dV/dt=dV/dR* dR/dt==>45=3πR²*dR/dt
==>dR/dt=45/(3πR² )
If R=4 then dR/dt=15/(π*16)=0.2984155...≈0.298

Without any certainty!!!