Question

Calculus Help!
1.)The radius r of a sphere is increasing at a rate of 3 inches per minute. Find the rates of change of the volume when r=9 inches and when r=36 inches.

2.)A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

Answer 1

Ah related rates..

my advice would be to first write down all relevant equations and all given equations:

you should know that the volume of a sphere is V=4/3pi*r^3
and you are given that the rate of change of the radius r'=3 in/min
and you want to solve for the rate of change of volume when r = 9 and when r = 36

now you want to find the rate of change of the volume, so start by differentiating your volume equation:
V' = 4pi*r^2*r'

you know r', and you are given r so now you just get to plug everything in and solve!

question 2 is very similar so give that one a shot on your own! Good luck

Answer 2

Thank you!!