Question

the radius of a sphere is increasing at a rate of 30 cm/min. determine the rate the volume is changing with respect to time when the radius is 15 cm

Answer 1

V = (4/3)πr³

dV/dt = 4πr²(dr/dt)

= 4π(15 cm)²(30 cm/min)

= 27,000π cm³/min