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