Question

TIme rate of Change Differential Calculus

A spherical balloon is being filled with a rate of 15feet^3 per sec. compute the time rate of change of the surface area of the balloon at the instant when its volume is 120 ft^3?

Answer 1

first when v=120
we have 4/3 pi r^3=120
solving for r
r^3=90/pi
r=(90/pi)^1/3
then we go to volume rate of change
dv/dt=4pi r^2 dr/dt
you need to solve for dr /dt
then plug in that to dA/dt =8rdr/dt

Answer 2

that will give the rate of change in surface area

Answer 3

need further assistant?