The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second.At the time when the radius of the sphere is 10 centimeters, what is the rate of increase of its volume?

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Answer 1 · 2015-10-15T16:07:18

The rate of increase would be #16pi#

The constant rate of the radius increase is 0.04 cm per second, which can be written as:

#(dr)/dt = 0.04#

The volume of a sphere is #4/3pir^3#
Differentiate this to find the rate of the change of volume:

#4pir^2(dr)/dt#
Plug in our variables:
#4pi(10)^2(0.04)#
This can evaluate to equal:
#16pi#

Hope this helps!