Answer to Question #198237 in Geometry for Angelo

Question #198237

A swimming pool is rectangular shape of length 12 m and width 5.5 m. It has a sloping bottom and is 1 m deep at one end and 3.6 m deep at the other end. The water from a full cylindrical reservoir 3.6 m in diameter and 10 m deep is emptied to the pool. Find the depth of water at the deep end.


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Expert's answer
2021-05-30T21:42:01-0400

Ans:-

The water from a full cylindrical reservoir 3.6 m in diameter and 10 m deep is emptied to the pool.

Volume of water in Cylinder

V=πr2h= 3.14×1.8×10=56.52 m3V=\pi r^2 h = \ 3.14\times 1.8\times 10 =56.52\ m^3

The cross section of the swimming pool is a trapezium with parallel sides 1 m and 3.6 m1 \ m \ and \ 3.6 \ m (depth of both ends) and 12 m\ 12\ m (length of pool) as the ⊥ r distance between ∥ sides.

The width of pool 5.55.5 m can be the length of cross section

Capacity of Swimming pool will be

C=12[(1+3.6)×12]×5.5=151.8 m3C=\dfrac{1}{2}[(1+3.6)\times 12]\times5.5=151.8\ m^3

Volume of Empty swimming pool 151.856.52=95.28 m3151.8-56.52=95.28\ m^3


Hence The height of depth side from the top will be

95.28=12[(1+x)×12]×5.5x=1.887 m95.28=\dfrac{1}{2}[(1+x)\times 12 ]\times5.5 \Rightarrow x=1.887\ m

Hence depth of water at the bottom end will be 3.61.887 = 1.713 m3.6-1.887 \ =\ 1.713\ m



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