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?

Question

15490 views around the world

You can reuse this answer
Creative Commons License

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!