Answer to Question #198237 in Geometry for Angelo

Question

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.

Answer 1

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

$V=\pi r^2 h = \ 3.14\times 1.8\times 10 =56.52\ m^3$

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

The width of pool $5.5$ m can be the length of cross section

Capacity of Swimming pool will be

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

Volume of Empty swimming pool $151.8-56.52=95.28\ m^3$

Hence The height of depth side from the top will be

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

Hence depth of water at the bottom end will be $3.6-1.887 \ =\ 1.713\ m$