To find the length of the hose from the top corner of the pool to the bottom corner farthest away, we can use the Pythagorean theorem in three dimensions. The length, width, and depth of the pool can be treated as the three dimensions of a rectangular prism.
Given:
- Length of the pool (l) = 30 feet
- Width of the pool (w) = 16 feet
- Depth of the pool (d) = 6 feet
The distance \( D \) from the top corner to the farthest bottom corner can be calculated using the formula:
\[ D = \sqrt{l^2 + w^2 + d^2} \]
Calculating step-by-step:
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Calculate \( l^2 \): \[ l^2 = 30^2 = 900 \]
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Calculate \( w^2 \): \[ w^2 = 16^2 = 256 \]
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Calculate \( d^2 \): \[ d^2 = 6^2 = 36 \]
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Now sum these values: \[ l^2 + w^2 + d^2 = 900 + 256 + 36 = 1192 \]
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Taking the square root: \[ D = \sqrt{1192} \approx 34.52 \text{ feet} \]
Therefore, the length of the hose from the top corner to the bottom corner farthest away is approximately 34.52 feet.
So, the answer is:
34.52 feet
1 answer