A spherical balloon with a 36cm diameter is being deflated. Its volume V is a function of its radius r according to

Question:

A spherical balloon with a 36 cm diameter is being deflated. Its volume V is a function of its radius r according to

As it's deflating, it is much easier to measure its radius than its volume. Suppose the radius of the balloon is cm at t seconds.

Explanation:

Given

Solving (a):  V'(4)

First, we determine V('r)

Differentiate w.r.t r

Substitute 4 for r and take

This means that the volume of the balloon when the radius is deflated to 4 seconds is 201.143 cm^3

Solving (b): r(4)

Substitute 4 for t in

This means that the radius of the balloon when at 4 seconds of deflation is 11.106 cm

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