Answer: dV/dt = 69,360πcm^3/min
Therefore, the rate of change of volume when r = 17 cm is = 69,360πcm^3/min
Step-by-step explanation:
The volume of a sphere is given by;
V = (4/3)πr^3
dV/dt = dV/dr × dr/dt
dr/dt = 60cm/min (given)
dV/dr = d/dr (4/3 πr^3) = 4πr^2
r = 17cm
So,
dV/dt = 4πr^2(dr/dt)
Substituting the values into the equation
dV/dt = 4π(17^2)(60)
dV/dt = 69,360πcm^3/min
Therefore, the rate of change of volume when r = 17 cm is = 69,360πcm^3/min
