Question

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 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.
a.)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.


b.)How much water do you need to fill just the pool without the fish tank, if the average depth is 4 feet?

Answer 1

The problem is modelled in the diagram below 

Question 1:
The largest area of the pool is half of the area of the circle

Area of circle = πr², where r is the radius given by 1/2 of the diameter
Area of circle = π(60)² = 11309.73355 feet

Area of half of the circle is 11309.73355/2 = 5654.866... ≈ 5654.87 feet (2dp)

Question b:

The area of the pool is the area of the circle subtracts the area of the triangle.

The area of the circle is 11309.73²

The area of the triangle is 1/2 (60×103.92) = 3117.6 feet²

The area of the pool is 11309.73 - 3117.6 = 7922.13 feet²

The volume of the pool = 7922.13 × 4 = 31688.52 feet³

Note: there isn't any information on the fish tank part so the answer above is assumed for the whole pool.