Acone has a height of h cm and a fixed value of base radius of 7cm. given that the volume of the cone is increasing at a rate of 5cm^3s^-1 find the rate of change of h.

Radius (r)=7 cm
height =h cm
volume (v)=(1/3)×πr²h
rate of change of h=dh/dt=?

Rate of change of volume:

↪dv/dt=(1/3)×d(πr²h)/dt
or, 5cm³/1s=(πr²/3)×(dh/dh)×(dh/dt)
or, 5 =(πr²/3)×1×(dh/dt)
or, (dh/dt)=15/(πr²)
=15/(π×7²)
=15/49π
↪(dh/dt) = 0.0974026cm/s➡ANS