Hey can some one pls explain this problem to me! tnx in advance
The swimming pool shown in Figure 1.54 is 3 ft. deep at the shallow end, 8 ft. deep at the deepest end, 40 ft. long, 30 ft. wide and the bottom is an incline plane. Express the volume V of water in the pool as a function of the height h of the water above the deep end.(hint: V will be a piecewise define function)
Hello, geeko!
A swimming pool is 3 ft. deep at the shallow end, 8 ft. deep at the deep end,
40 ft. long, 30 ft. wide, and the bottom is an incline plane.
Express the volume of water in the pool as a function of the height
of the water at the deep end. (Hint: will be a piecewise-defined function)Code:40 - * - - - - - - - - - - - - - - - - - * : | | 3 | | 3 : | 40 | - * - - - - - - - - - - - - - - - - - * : | x * : + - - - - - - - - - - - * 6 |:::::::::::::::::* : h|:::::::::::* : |:::::* - *
For the first six feet, the volume of water is a triangular prism.
. . Its volume is: .
From the similar right triangles: . .[1]
The area of the triangle is: .
Substitute [1]: .
Then the volume is: .
. .
For the last three feet of water, the bottom (triangular) portion is already filled.
. . It contains: . ft³ of water.
The upper portion is a rectangular slab of water:
. . length 40, width 30, and height
Its volume is: . ft³.
The total volume is: .
. .
Therefore: .