calculus ques.?

Question

a spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 30 centimeters and when it is 60 centimeters?
show the steps

Answer 1

The volume of a sphere of radius r is

V = (4/3)π r³

You are given that dV/dt = 800 and you are asked to find dr/dt when r=30 and r=60.

Differentiate both sides of the volume formula with respect to t:

dV/dt = 4π r² dr/dt

Solving for dr/dt,

dr/dt = (dV/dt)/(4π r²)