Question

A rectangular swimming pool is 48 m long and 20 m wide. The shallow edge of the pool is 1 m deep. For every 2.6 m that one walks up the inclined base of the swimming pool, one gains an elevation of 1 m. What is the volume of water (in cubic meters), in the swimming pool? Assume that the pool is filled up to the brim.

Accepted Answer

D. Slope ratio: $2.6^2 = 1^2 + b^2 \implies b^2 = 6.76 - 1 = 5.76 \implies b = 2.4$. For length $48$ m, gain in elevation $= 48 / 2.4 = 20$ m. Deep end depth $= 1 + 20 = 21$ m. Cross-sectional area $= 	ext{Rectangle}(48 	imes 1) + 	ext{Triangle}(\frac{1}{2} 	imes 48 	imes 20) = 48 + 480 = 528 	ext{ m}^2$. Volume $= 528 	imes 20 = 10560 	ext{ m}^3$.

Volume of Swimming Pool

Explanation

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