Plz explain, thx

Question

The radius r, height h, and volume V of a cone are related by the equation  How is  related to  and  if neither r nor h is constant?

Answer 1

V= hpir^2/3

use the product rule

1st term times derivative of 2nd term plus

2nd term times derivative of 1st term

with the derivative with respect to time or t

let 1st term = h

let 2nd term = pir^2/3

V'= dV/dt = h(2pir/3)(dr/dt) + (pir^2/3)(dh/dt)

dV/dt = (2rpi/3)[(h(dr/dt)) +r(dh/dt)]

V' = (2rpi/3)[hr' +rh']