Mathematics

A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in litres required to fill the pool.

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Length of the pool (L) = 40 m

Width of the pool (W) = 15 m

Depth at the shallow end = 1.5 m

Depth at the deep end = 3 m

The cross-section of the pool is a trapezium with:

Parallel sides (depths) as 1.5 m and 3 m.

Height of the trapezium equal to the width of the pool (15 m).

Area of the trapezium = $\dfrac{1}{2}$ x (sum of parallel lines) x height

= $\dfrac{1}{2}$ x (1.5 + 3) x 15 m²

= $\dfrac{1}{2}$ x 4.5 x 15 m²

= $\dfrac{1}{2}$ x 67.5 m²

= 33.75 m²

Volume of the pool = Area of the trapezium x length

= 33.75 x 40 m³

= 1350 m³ = 13,50,000 litres

Hence, the amount of water required to fill the swimming pool is 13,50,000 litres.

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