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Answer :
Final answer:
To calculate the volume of the pool, we use the formula for the volume of a cylinder, convert the result to cubic inches, and then convert to gallons. The final answer, rounded to the nearest integer, is 6671 gallons.
Explanation:
The student wants to find the volume of a circular swimming pool in gallons. Firstly, we calculate the pool's volume in cubic feet using the formula for the volume of a cylinder V = πr2h, where r is the radius and h is the depth. The diameter of the pool is 17.8 feet, so the radius is half of that, which is 8.9 feet. Plugging in the values, we get V = π(8.92)(3.4). Calculating this gives a volume in cubic feet. We then convert this volume to cubic inches by multiplying by 1728 (since 1 cubic foot is 1728 cubic inches). Finally, we divide by 231 to convert from cubic inches to gallons, as 1 gallon is equivalent to 231 cubic inches.
Now performing the calculations: The volume in cubic feet is approximately V = π(8.92)(3.4) ≈ 891.5 cubic feet. To convert to cubic inches, multiply by 1728 to get 891.5 * 1728 ≈ 1541172 cubic inches. Finally, to convert to gallons, divide by 231 to get 1541172 / 231 ≈ 6671.3 gallons, which we round to the nearest integer, giving us a final answer of 6671 gallons.
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