SOLUTION: I am having trouble with this problem. An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right trian

Question 1041413: I am having trouble with this problem.
An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The circumference of the pool circumscribes the triangle central area and the center of the circle is a point on the hypotenuse (longest side) of the triangle. The building permit the resort obtained requires that the resort state how much water the pool will hold so the city can manage the resort�s water rights effectively.
1. The resort owner wants to line the edge of the pool with 24k gold leaf. Explain how to determine how many linear feet of gold leaf you should plan to cover. (Don�t forget to cover the edges of the circular part of the pool and also the straight edges outlined by the triangle.)
2. As the land surveyors lay out the pool before digging, determine what method they should use to ensure the circular pool circumscribes the triangular restaurant.
3. Inset in the floor of the restaurant is a circular shark tank. The shark tank is inscribed in the triangle area. Describe how to find the center point for that circle.
4. If the pool�s depth averages 4 feet, how much water will it take to fill the pool? (Hint: the volume of a cylinder is the area of the base times the depth.)
5. If the city ordinances only allow the resort to use 30,000 cubic feet of water in the pool (ignore the shark tank), show how to calculate the maximum depth the pool can be to stay under the 30,000 cubic foot threshold.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The triangle is inside the circle with the vertices of the triangle on the circle - since the center of the circle is on the hypotenuse, the hypotenuse is the diameter(D) of the circle
:
D = 120 feet
:
circumference of the circle = 22/7 * 120 = 377.14 feet
perimeter of triangle = 120 + 60 + 103.92 = 283.92
:
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1) total distance around circle + triangle = 661.06 feet
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:
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2) the vertices of the triangular central area must lie on the
circular pool - construct perpendicular bisectors of two sides
of the triangular area, where they intersect is the center of
the circular pool, the distance from the center to any one of
the vertices of the triangular area is the radius of the
circular pool
**************************************************************
:
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3) the intersection of the angle bisectors of the triangular area
is the center of the shark tank
*****************************************************************
:
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4) volume of pool = ((pi * 60^2) - area of triangle) * 4 =
(11314.285) - (1/2 * 103.92 * 60) * 4 = 32786.74 cubic feet
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:
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5) 8196.685 * x < 30000
x < 3.66 feet
average depth must be less than 3.66 feet
*****************************************

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