Question

A spherical balloon is expanding at the rate of 60pi cubic inches per second. How fast is the surface area of the balloon expanding when the radius of the balloon is 4 in?

Answer 1

30

Explanation:

`V = 4/3 pi r^3` so `dot V = 4 pi r^2 dot r`

`A = 4 pi r^2` so `dot A = 8 pi r dot r`

that means `dot r = (dot A )/( 8 pi r) = (dot V )/( 4 pi r^2)`

so `dot A = (2 dot V )/( r) = (2*60)/4 = 30` sq in per sec