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.
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?
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?
1 answer:
The diagram below illustrates the issue at hand.
Question 1:
The maximum area of the pool equals half the area of the circle.
To calculate the area of the circle: Area = πr², with r being half of the diameter.
Thus, Area of circle = π(60)² = 11309.73355 square feet.
Therefore, the area representing half the circle amounts to 11309.73355/2 = 5654.866... ≈ 5654.87 square feet (rounded to 2 decimal places).
Question b:
To find the pool's area, we take the circle's area and subtract the triangle's area.
The area of the circle is 11309.73 square feet.
For the triangle's area calculation: 1/2 × (60×103.92) = 3117.6 square feet.
The area of the pool thus operates as 11309.73 - 3117.6 = 7922.13 square feet.
Calculating the pool's volume: 7922.13 × 4 = 31688.52 cubic feet.
Note: Information related to the fish tank is unavailable, so the above calculation focuses solely on the entire pool's volume.
Question 1:
The maximum area of the pool equals half the area of the circle.
To calculate the area of the circle: Area = πr², with r being half of the diameter.
Thus, Area of circle = π(60)² = 11309.73355 square feet.
Therefore, the area representing half the circle amounts to 11309.73355/2 = 5654.866... ≈ 5654.87 square feet (rounded to 2 decimal places).
Question b:
To find the pool's area, we take the circle's area and subtract the triangle's area.
The area of the circle is 11309.73 square feet.
For the triangle's area calculation: 1/2 × (60×103.92) = 3117.6 square feet.
The area of the pool thus operates as 11309.73 - 3117.6 = 7922.13 square feet.
Calculating the pool's volume: 7922.13 × 4 = 31688.52 cubic feet.
Note: Information related to the fish tank is unavailable, so the above calculation focuses solely on the entire pool's volume.
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