Question

A sphere is increasing in volume at the rate 3pi cm^3/s. At what rate is its radius changing when the radius is 1/2 cm?

Answer 1

V=4/3 pi r^3
dV/dt=d(4/3pi r^3)/dt

Answer 2

Now, use chain rule to find dr/dt

Answer 3

can u?

Answer 4

dr/dt = 1/(4pi r^2) * (dV/dt)

Answer 5

Substitute 1/2 in for r?

Answer 6

yes

Answer 7

and dV/dt=3pi cm^3/s

Answer 8

dr/dt = 1/(4pi*((1/2)^2))*3pi cm^3/s = 3 cm^3/s Thank you!! :)

Answer 9

welcome