The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is the volume changing when the radius is 14 centimeters?

Note: The volume of a sphere is given by V=(4/3)\pi r^3.

Rate of change of volume =

Applying implicit differentiation, it is found that the volume is changing at a rate of 9852 cubic centimetres per minute.

The volume of a sphere of radius r is given by:

Applying implicit differentiation, the rate of change is given by:

We are given that:

Then

The volume is changing at a rate of 9852 cubic centimetres per minute.

A similar problem is given at link

The rate of change in volume is .

Step-by-step explanation:

Given:

radius

We need to find the rate of change of Volume

Solution:

Now We can say that:

Volume of sphere is given by:

Now taking derivative on both side we get;

But   and so we get;

Rate of change of volume =

Hence the rate of change in volume is .

answer: (1,3) and (-2,0) i think.

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