An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a r

Question

1 month ago

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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 r

ight triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The vertices of the triangle are points on the circle. The hypotenuse of the triangle is the diameter of the circle. 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.
The resort owner wants to line the largest circular edge of the pool with 2 inches of 24K gold leaf. Explain how to determine how many linear feet of gold leaf you should plan to cover.

What is the area of the largest section of the pool? Explain if you feel this area would be large enough to add a waterslide.

Inset in the floor of the restaurant is a circular fish tank with a diameter of 10 feet. The fish tank is concentric with the pool. Describe how to find the center point for that circle.

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.)

City ordinances only allow the resort to use 40,000 cubic feet of water in the pool without the fish tank. Show how to calculate the maximum depth the pool can be to stay under the 40,000-cubic-foot threshold.

How much water do you need to fill just the pool without the fish tank, if the average depth is 4 feet? Explain the difference in your calculations for questions 5 and 6. Does it change the maximum average depth of your water?

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-02-26T22:34:04+03:00

The triangle is positioned within the circle, with its vertices lying on the circle's edge - since the center of the circle is located on the hypotenuse, that hypotenuse serves as the diameter (D) of the circle.

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D = 120 feet

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Calculating the circumference of the circle gives: 22/7 * 120 = 377.14 feet.

The perimeter of the triangle is calculated as 120 + 60 + 103.92 = 283.92

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1) The combined distance around both circle and triangle totals 661.06 feet.

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2) The vertices for the triangle's central area must touch the circular pool - to find the center of the pool, draw perpendicular bisectors from two of the triangle's sides; where they meet is the center.

The distance from the center to any vertex of the triangular area represents the radius of the

circular pool.

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3) The intersection of the triangle's angle bisectors indicates the center of the shark tank.

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4) The pool's volume is calculated as ((π * 60^2) - area of triangle) * 4 =

(11314.285) - (1/2 * 103.92 * 60) * 4 = 32786.74 cubic feet.

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5) 8196.685 * x < 30000

x < 3.66 feet

The average depth needs to be below 3.66 feet

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