Physics—Volume Analysis: Suppose a spherical balloon is being inflated with the radius inc...

Physics—Volume Analysis: Suppose a spherical balloon is being inflated with the radius increasing at an average rate of 1.3 inches per second.

(a) Write the radius r(t) as a function of time t. Assume that when t = 0, r = 0.

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(b) The volume of a sphere as a function of its radius is given by . Simplify V(t) = V(r( t)), and interpret the meaning of this composition.

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(c) Evaluate V(t) when t = 6 and interpret the result.