# calculus

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.

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1. 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

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2. 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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