Related Rates - A Paraboloid Container

Question

A paraboloid container is being filled with fluid at the rate of 4.5 cubic feet per minute. At what rate is the level of fluid changing when the depth is 2.5 feet? The ratio of the radius to the height of the container is 3 : 7.

`V = 1/2 pir^2h`

A) 0.33 ft./min

B) 0.57 ft./min

C) 1.12 ft./min

D) 2.62 ft./min

Answer 1

r:h = 3:7, i.e. h=7r/3

Substitute this ratio into the given equation for volume.

Differentiate the volume equation with respect to t.

Then substitute the rate of change of volume into the equation and solve for the rate of change of height.