Assume that the radius 𝑟 of a sphere is expanding at a rate of 12 in./min.

Question

12 in./min.The volume of a sphere is 𝑉=4/3pi*r^3
Determine the rate at which the volume is changing with respect to time when 𝑡=7 min.assuming that 𝑟=4 @ 𝑡=0

Answer 1

r = 4 + 12t
v = 4/3 πr^3
dv/dt = 4πr^2 dr/dt
at t=7,
dv/dt = 4π(4+12*7)^2 (12) = ___