Question

A swimming pool is 50 meter long and 15 meters wide. Its shallow and deep ends are `1 1/2` meters and `4 1/2` meters deep respectively. If the bottom of the pool slopes uniformly, find the amount of water required to fill the pool.

Answer 1

Given:

Length = 50 m, Width = 15 m.

Depth at shallow end = `1 1/2` m = 1.5 m.

Depth at deep end = `4 1/2` m = 4.5 m.

Bottom slopes uniformly (cross-section is a trapezoid).

Step-wise calculation:

1. Area of trapezoidal cross-section

= `1/2` × (Sum of parallel sides) × (Distance between them)

= `1/2 xx (1.5 + 4.5) xx 15`

= `1/2 xx 6 xx 15`

= 3 × 15 

= 45 m²

2. Volume = (Area of cross-section) × (Length)

= 45 m² × 50 m

= 2250 m³

3. Conversions:

In litres: 2250 m³ × 1000 = 2,250,000 litres.

In US gallons (1 m³ = 264.172 gallons):

2250 × 264.172 = 5,94,387 gallons

The pool requires 2250 cubic metres of water to fill which is 2,250,000 litres = 5,94,387 US gallons.