The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100 mm

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

Step-by-step explanation:

Volume of a sphere:

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

How fast is the volume increasing:

To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So

The radius of a sphere is increasing at a rate of 2 mm/s.

This means that

How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?

Radius is half the diameter, so

Then

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

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