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 80 mm? (Round your answer to two decimal places.)

Answer 1

Start with the formula for volume of a sphere.

V=4/3πr³

Now, take the derivative of this equation with respect to time.

dV/dt = 4/3π (3)r² dr/dt Simplify

dV/dt = 4π r² dr/dt Now we can identify what is given in the problem and what we are solving for.

dV/dt is what they are asking us to solve for.

d = 80, we need r for the formula, r = 40

dr/dt = 2

dV/dt = 4π (40)² (2)

dV/dt = 12800π mm³/s