Thread: Rates of change

Gas escapes from a spherical balloon at rate of 720cm^3 per second. Find the rate of change of the curface area when the radius is 36cm.

Help me please . thank you very very much

Originally Posted by helloying

Gas escapes from a spherical balloon at rate of 720cm^3 per second. Find the rate of change of the curface area when the radius is 36cm.

What is the formula for the volume V of a sphere having a radius of r?

What is the formula for the surface area SA of a sphere having radius r?

When r = 36, what is the surface area?

Note that you are given that dV/dt = -720.

Differentiate the "volume" formula with respect to time "t".

Plug in the known values for dV/dt and r. Solve for dr/dt.

If you get stuck, please reply showing how far you have gotten, starting with the "volume" and "surface area" formulas. Thank you!

Originally Posted by helloying

Gas escapes from a spherical balloon at rate of 720cm^3 per second. Find the rate of change of the curface area when the radius is 36cm.

Help me please . thank you very very much

You need to know the volume V and the surface area A of the sphere with radius r. Then differentiate both sides with respect to t.