Monday

March 2, 2015

March 2, 2015

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

- Math -
**Steve**, Friday, March 2, 2012 at 4:42pmLuckily, 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 4:58pmThe 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 ...

math..word problem - A landscaper dug holes. It takes him 1 hour to dig a hole 2...

Math - A landscaper is digging holes it takes him one hour to dig a hole 2 feet ...

Trigonometry - 1. Brothers Bob and Tom buy a tent that has a center pole of 6.25...

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...

math - a certain company makes inflatable swimming pools that come in four ...