Question

air is being pumped into a spherical balloon at a rate of 2 cubic meters per minute. Find the rate of change of the radius when the radius is 3 meters. v=4/3pir^3

Answer 1

were given the change of the volume V as a change in time. dV/dt = 2 m^3/min

if we take the derivative of Volume

d/dc (V) = d/dx (3piR^3)

dV/dt = 4piR^2 dR/dt

R = 3 m
2 = 4pi(3)^2 dR/dt

2 = 36pi dR/dt

dR/dt = 1/18pi