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## Homework Statement

Air is being pumped into a spherical balloon so that its volume increases at a rate of 70 cm

^{3}/s. How fast is the surface area of the balloon increasing when its radius is 5 cm

^{3}?

## Homework Equations

A ball with radius

*r*has the following volume (V) and surface area (S):

V = (4/3)(πr

^{3})

S = 4πr

^{2}

## The Attempt at a Solution

The problem seems to be asking for dS/dt at r = 5. dV/dt appears to be equivalent to S.

dS/dt = (d/dt)(4πr

^{2})

dS/dt = 8πr(dV/dt) <--- This step is the one that's really bugging me, especially that dV/dt tagged onto the end.

dS/dt = 8π5(70)

dS/dt = 2800π

dS/dt = 8796.459

Which is apparently incorrect. I'm having a lot of trouble grasping these and other related rate problems, mainly because I am not sure how to properly set up the equations and every tutorial I've found on the subject (including my textbook) simply breeze over that step by saying "Find an equation that describes the given relationship."

Any help is much appreciated.