Question

Suppose the radius of a spherical balloon is growing at the rate of 50 cm/s, so how quickly is the volume increasing when the radius is 6 cm?

Answer 1

well from the previous question we know that
V = (4/3) pi r^3
then derivative of V = V' = 4 pi r^2 r'

we were then given that the radius increases at a rate of 50
so rate of radius = derivative of radius = r' = 50
and radius = 6
then plug that in

so V' = 4 pi (6)^2 (50)
= ?

Answer 2

7200pi

Answer 3

yup :)

Answer 4

that's it?

Answer 5

Thanks, buddy!

Answer 6

you're welcome :)