Posted by **Kelly** on Wednesday, October 16, 2013 at 10:49pm.

You are blowing air into a spherical balloon at a rate of 7 cubic inches per second. The goal of this problem is to answer the following question: What is the rate of change of the surface area of the balloon at time t= 1 second, given that the balloon has a radius of 3 inches at that instant?

(a) Next write a formula relating the changing volume V(t) of the sphere to the changing radius r(t), and differentiate that formula with respect to t. Using what you know about V'(t) and r(1), find the rate of change of the radius at t=1 sec:

(b) Finally, write a formula relating the changing surface area S(t) of the sphere to the changing radius r(t), and differentiate that formula with respect to t. Use what you know about r(1) and r'(1) to determine the rate of change of the surface area at t=1 sec:

## Answer This Question

## Related Questions

- calculus - A spherical balloon is being inflated at a rate of 10 cubic inches ...
- Calculus - A spherical balloon is being inflated at a rate of 10 cubic inches ...
- calculus - Air is being pumped into a spherical balloon so that its volume ...
- Calculus - Air is being pumped into a spherical balloon so that its volume ...
- related rates problem-calculus - A spherical balloon is being filled with air in...
- Calculus - Air is being pumped into a spherical balloon so that its volume ...
- calculus - is my answer to this question correct A spherical balloon is losing ...
- Calculus - A spherical water balloon is being filled with water at the rate of ...
- AP calculus AB - A spherical balloon is being filled with air in such a way that...
- help on calculus - A spherical balloon is being filled with air in such a way ...

More Related Questions