A spherical balloon with radius r inches has a volume V(r)=4/3(pi)r^3. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r+1...

A spherical balloon with radius r inches has a volume V(r)=4/3(pi)r^3. Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r+1 inches.

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The amount of air required to inflate a spherical balloon from radius r to radius (r+1) is required:

The difference in the volumes is:

`V_2-V_1=4/3 pi (r+1)^3-4/3 pi r^3`

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