Posted by **Anonymous** on Friday, March 25, 2011 at 7:06pm.

A spherical balloon is being inflated at a rate of 10 cubic inches per second. How fast is the radius of the balloon increasing when the surface area of the balloon is square inches? Enter your answer correct to 3 decimal places.

- calculus -
**Damon**, Friday, March 25, 2011 at 7:12pm
well, you forgot to say what that area was but anyway

for a sphere

V = (4/3) pi r^3

A = dV/dr = pi r^2

dV/dt = dV/dr * dr/dt = pi r^2 dr/dt

dV/dt = 10 given

so

10 = pi r^2 dr/dt

put in the r from the surface area you forgot to type and solve for dr/t

- calculus -
**Anonymous**, Friday, March 25, 2011 at 7:15pm
OOps How fast is the radius of the balloon increasing when the surface area of the balloon is 2pi square inches?

## Answer This Question

## Related Questions

- 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 ...
- Calculus - A spherical balloon is being inflated and the radius of the balloon ...
- Calculus - A spherical water balloon is being filled with water at the rate of ...
- Calculus - a spherical balloon is inflated with gas at the rate of 500 cubic ...
- calculus - A spherical balloon is leaking air at 2 cubic inches per hour. How ...
- Calculus - Air is being pumped into a spherical balloon so that its volume ...
- AP calculus AB - A spherical balloon is being filled with air in such a way that...
- Calculus - A spherical balloon is being inflated and the radius is increasing at...

More Related Questions