Posted by **Greg** on Friday, March 2, 2012 at 3:07pm.

A swimming pool is 40 feet long, 20 feet wide, 8 feet deep at the deep end, and 3 feet deep at the shallow end; the bottom is rectangular. If the pool is filled by pumping water into it at the rate of 40 cubic feet per minute, how fast is the water level rising when it is 3 feet deep at the deep end?

- Math -
**Steve**, Friday, March 2, 2012 at 4:42pm
Luckily, all we are working with is a triangular section, until the water is 5' deep; then we have to work with a trapezoid.

Anyway, looking at the side of the pool, when the water is y' deep, we have a triangular prism with a cross-section that is y by y/8 (since the pool bottom is a line with slope 5/40 = 1/8

So, the volume is

v = 1/2 * y*y/8 * 20 = 5y^2/4

dv/dt = 5y/2 dy/dt

40 = 5*3/2 dy/dt

dy/dt = 16/3 ft/min

- Math -
**Emory**, Thursday, July 3, 2014 at 4:58pm
The error in Steve's answer is that v = 1/2 * y * 8y * 20. The height of the line of the pool bottom is determined by h = 1/8 *l, so the length of the cross section is 8h, not h/8. The correct answer is 1/12 ft^3/min.

1/12 ft^3/min is the selected answer in Varberg Early Transcendentals for this problem. Please check answers carefully.

## Answer this Question

## Related Questions

- Calculus - A swimming pool is 40 feet long, 20 feet wide, 8 feet deep at the ...
- Precalculus - A swimming pool is 3 feet deep in the shallow end. The bottom of ...
- geometry - A swimming pool is 3 ft deep in the shallow end the bottom of the ...
- DIFF CALCULUS - A swimming pool is 12 meters long, 6 meters wide, 1 meter deep ...
- Math - a pool 5 feet deep with a diameter of 40 feet is filled with water in 50 ...
- CALCULUS - Hi guys can you help me! Please teach me step by step.. I really need...
- Trigonometry - 1. Brothers Bob and Tom buy a tent that has a center pole of 6.25...
- math - a certain company makes inflatable swimming pools that come in four ...
- Calculus - A swimming pool is 60ft long by 25ft wide. Its depth varies uniformly...
- Math - A swimming pool that is 100 feet in length by 10 feet deep and 40 feet ...