Question

A spherical balloon is inflated with gas at a rate of 5 cubic centimeters per minute. How fast is the radius of the balloon changing at the instant when the radius is 4 centimeters? The volume VV of a sphere with a radius rr is V=43πr

Answer 1

Explanation:

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Answer 2

0.025 cm/min

Explanation:

The volume rate of change is

`(dV)/(dt) = 5`

We are to determine the rate of change of the radius. This is given by

`(dr)/(dt)=(dV)/(dt)/(dV)/(dr)`

The volume of a sphere is given by

`V = (4)/(3)\pi r^3`

Hence,

`(dV)/(dr) = 4\pi r^2`

Therefore,

`(dr)/(dt)=(5)/(4\pi r^2)`

When r = 4,

`(dr)/(dt)=(5)/(4\pi 4^2)=(5)/(64\pi)`

`(dr)/(dt)=0.025 \text{ cm/min}`