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), ?->(Show Answer!)

1. 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.v

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By: anil on 05 May 2019 02.37 am

For every 2.6 m that one walks along the slanting part of the pool, there is a height of 1 m that is gained. => $$frac{AC}{BC} = frac{2.6}{1}$$ => $$AC = 2.6 imes BC$$ Also, dimensions of cuboidal part = $$48 imes 20 imes 1$$ In $$ riangle$$ ABC => $$(AC)^2 = (AB)^2 + (BC)^2$$ => $$(2.6 imes BC)^2 = (48)^2 + (BC)^2$$ => $$6.76 (BC)^2 - (BC)^2 = 2304$$ => $$(BC)^2 = frac{2304}{5.76} = 400$$ => $$BC = sqrt{400} = 20$$ m $$ herefore$$ Volume of water in the pool = Volume of cuboid + Volume of triangle = $$(l imes b imes h) + (frac{1}{2} imes AB imes BC) imes height$$ = $$(48 imes 20 imes 1) + (frac{1}{2} imes 48 imes 20 imes 20)$$ = $$960 + 9600 = 10560 m^3$$

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