The volume of a sphere is increasing at a rate of 5 cm^3/s. Find the rate of change of its surface area when its volume is 500pi/3 cm^3.

Answer 1

v = 4/3 pi r^3
a = 4pi r^2

dv/dt = 4pi r^2 dr/dt
da/dt = 8pi r dr/dt

when v=500pi/3, r=5

5 = 100pi dr/dt
dr/dt = 1/(20pi)

da/dt = 8pi r dr/dt
= 8pi*5/(20pi)
= 2

Answer 2

The volume of a sphere increase at the rate of 20cm/sec . Find the rate of change of its surface area when it's radius 5cm