A cone 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