The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm

The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere is given by the following equation:

In which r is the radius.

Implicit derivatives:

This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So

The radius of a sphere is increasing at a rate of 4 mm/s.

This means that

How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm?

This is when . So

The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.

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