hydrogen is being pumped into a spherical balloon at the rate of 250 cubic inches per minute. in a and b, you must provide an equation with their proper numerical factors when showing the relationships inquired

Question

A) write an equation showing the relationship between the rates at which the volume of the balloon is changing while the radius is changing?
B. write an equation showing the relationship between the rates at which the volume of the ablloon is changing while the area is changing?
C. at what rate is the radius increasing when the volume of the balloon is 972pi incles?

Answer 1

Start with
V=4/3 PI r^3 then take the derivative of each side with respect to time

dV/dt= 4/3 PI * 3r^2 dr/dt

Now do the same with the surface area equation.

For the last, what is radius when V is 972? Put that r into the dV/dt equation.