A circular swimming pool is 17.5 ft in diameter and 3.5 ft deep. Determine the volume, \( v \), of the pool in gallons if one gallon is 231 cubic inches. Round the answer to the nearest integer.

Question

23-02-2024
Mathematics

High School

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A circular swimming pool is 17.5 ft in diameter and 3.5 ft deep. Determine the volume, \( v \), of the pool in gallons if one gallon is 231 cubic inches. Round the answer to the nearest integer.

Answer :

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EugeneMarie EugeneMarie · Answer 1 · 2024-09-05T18:06:15-04:00

Final answer:

We need to find the volume of the pool using the formula of the volume of a cylinder, convert this to gallons, and then round to the nearest integer.

Explanation:

To solve this problem, we first need to find the volume of the circular pool in cubic feet. The formula for the volume of a cylinder, which is the shape of the pool, is V = π(radius)² * height. Since we know the diameter of the pool is 17.5ft, the radius would be 17.5ft / 2 = 8.75ft. So the volume in cubic feet would be V = π(8.75ft)² * 3.5ft.

Once we have the volume in cubic feet, we need to convert this to gallons. There are approximately 7.48052 gallons in one cubic foot. So we multiply our volume in cubic feet by 7.48052, to get the volume in gallons. However, we're also asked to convert further, to gallons from cubic inches, so we need to know that 1 gallon equals 231 cubic inches. You would use dimensional analysis, a mathematical technique for converting between units, to carry this out.

Lastly, round up the final number to its nearest integer to get the final answer.

Learn more about Volume calculation and conversion here:

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