The radius of a spherical is decreasing at a constant rate of 3 cm per second. Find, in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5cm.

DV/dt = 942 cm³/sec (decreasing)

Step-by-step explanation:

Volume of the sphere V = 4/3π*r³

r ⇒ r (t)

DV / dt = DV/dr * Dr/dt so

DV/dt = 4*π*r²*Dr/dt

and we know Dr/dt = - 3 cm/sec and r = 5 cm

Then radius decreasing V also decreases

by substitution

DV/dt = - 4*π * (5) ² * (3)

DV/dt = - 942 cm³/sec