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Answer:
The volume increases at a rate of
Step-by-step explanation:
The rate of change of the radius with respect to time is 4 mm / s.
So:
Now we must find a relationship between the volume of a sphere and its radius.
The equation of the volume of a sphere is:
So:
The diameter of the sphere is 100 mm. Therefore its radius is 100/2 = 50 mm.
So:
The volume increases at a rate of :
40000 π mm ^ 3 / s = 125663.71 mm^3/s