Homework Help: calculus

Posted by Jasmine on Thursday, April 19, 2012 at 12:00am.

A swimming pool is a rectangular solid 15 ft wide, 40 ft long, and at most 4 ft deep. Water is being added to the pool at the rate of 25 cubic ft per minute. How fast is the water rising when there is 1800 cubic ft of water in the pool?

calculus - Steve, Thursday, April 19, 2012 at 12:22pm
since the pool is a rectangular solid, it has a cross-section of constant size.

the pool is 15x40 = 600 ft^2

Thus, each ft of depth adds 600ft^3 of volume.

So, at 25ft^3/min, the height rises 25/600 = .0417 ft/min

Now, since this is for calculus class, they must want a solution involving related rates.

v = 40*15*x = 600x when the water is x feet deep.

dv/dt = 600 dx/dt
25 = 600 dx/dt
dx/dt = 25/600 = .0417

Answer this Question

Related Questions

physics - Water flows into a swimming pool at a rate of 9.59 gal/min. If the ...
physics - Please help me solve !!! Water flows into a swimming pool at the rate ...
geometry - the perimeter of a rectangular swimming pool is 40 ft. the length of ...
math - The length of a swimming pool is 22 ft. The width is 40 ft. If the volume...
Geometry. - A park has a circular swimming pool. The diameter of the pool is 18 ...
math - A deck is being built around a rectangular swimming pool. The swimming ...
math question - A pool company will install a round swimming pool in the middle ...
Math - A rectangular wimming pool is 40 ft wide and 45 ft long. It is surrounded...
math - A 20-ft by 40-ft swimming pool is surrounded by a deck d feet wide. What ...
Math - A rectangular field is to be enclosed with 1270 ft of fencing. If the ...

For Further Reading

First Name:
School Subject:
Answer: