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?

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