SOLUTION: A swimming pool is 100 feet long and 50 feet wide. It is 7 feet deep at the deep end and has a beach entry(0feet deep) at the shallow end. The bottom of the pool has a constant slo

Question 689451: A swimming pool is 100 feet long and 50 feet wide. It is 7 feet deep at the deep end and has a beach entry(0feet deep) at the shallow end. The bottom of the pool has a constant slope. What is the surface area of the inside of the pool? If it helps the water capacity is 17500ft^3 or 130 000 US gallons. The answer in the answer key is 6062ft^2 but I have no idea how they got there.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A swimming pool is 100 feet long and 50 feet wide. It is 7 feet deep at the deep end and has a beach entry(0feet deep) at the shallow end. The bottom of the pool has a constant slope. What is the surface area of the inside of the pool?
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A cross-section of the water in the pool from the "beach"
to the deepest point is a right triangle with height = 7 ft,
and base = 100 ft.
------
The area of that rectangle is (1/2)7*100 = 350 sq. ft.
2 sides of the pool are each 350 sq. ft.
----
The wall at the deepest point has area = 7*50 = 350 sq. ft
---
The length of the bottom of the pool is sqrt[100^2 + 7^2] = 100.25 sq. ft
The area of the bottom of the pool is 100.25*50 = 5012 sq. ft
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Adding the 3 walls and the bottom surface you get 3(350) + 5012 = 6062.24
sq ft.
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Cheers,
Stan H.

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