HELP ON CALCULUS PROBLEM

[math guy]

A swimming pool is 40 feet long, 20 feet wide, 4 feet deep at the shallow end, and 9 feet deep at the deep end. water is being pumped into the pool at 10 cubic feet per min, and there is 4 feet of water at teh deep end.

A- WHAT PERCENTAGE OF THE POOL IS FILLED?
B- AT THUE RATE IS THE WATER LEVEL RISING?

 

[skeeter]

for h < 5 at the deep end, the water forms a triangular prism (wedge).

looking at the pool from its side, let the depth at the deep end be "h" and let the horizontal length of the water surface be "L"

using similar triangles, L/h = 40/5 = 8, so L = 8h

volume of the water in the pool when h < 5 at the deep end is V = (1/2)(8h)(h)(20) = 80h[sup:1m4k75sy]2[/sup:1m4k75sy].

you now should be able to find solutions for (a) and (b).