SOLUTION: A swimming pool is 12 feet long and 10 feet wide. At its deepest, it is 7 feet deep. A slope 5 feet long links the deep end to the shallow end. Jonathan wants to fill the pool with

Question 1134586: A swimming pool is 12 feet long and 10 feet wide. At its deepest, it is 7 feet deep. A slope 5 feet long links the deep end to the shallow end. Jonathan wants to fill the pool with 800 cubic feet of water. Is this possible? Explain.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the minimum volume of the pool is 12 * 10 * 2 = 240 cubic feet and the maximum volume of the pool is 12 * 10 * 7 = 840 cubic feet.

since 800 cubic feet is somewhere between 240 and 840 cubic feet, than 800 cubic feet of water could fill the pool.

to fill the pool with exactly 800 cubic feet of water, the sloped section would have to have a cross section of a right triangle where the vertical leg would have to be .4206601574 feet and the horizontal leg would have to be 4.982273079 feet and the hypotenuse would have to be 5 feet.

the slope of 5 feet in length that links the deep end of the pool to the shallow end of the pool if the hypotenuse of this right triangle.

the formula for the volume of the pool would be 10 * 12 * (7 - .4206601574) + 10 * 1/2 * .420601574 * 4.982273079 = 800 cubic feet.

so, if the minimum depth of the pool is 6.579339843 feet and the sloped section of the pool is 5 feet and the horizontal distance of the sloped section of the pool is 4.982273079 feet, and the maximum depth of the pool is 7 feet, then the volume of the pool will be exactly 800 cubic feet.

the following diagram gives you a vertical cross section of the pool.

$$$

the area of this vertical cross section will be 80 square feet.

the volume of the pool will be 10 * the area of the vertical cross section, making the volume equal to 800 cubic feet.

bottom line:

yes it is possible that the volume of the pool is exactly 800 cubic feet which will allow the 800 cubic feet of water to completely fill it.

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