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Answer:
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.