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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.

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