Question

The surface of a swimming pool is 50-meter long and 20-meter wide rectangle. The pool is 1 meter deep at the shallow end and 8 meters deep at the other end. Find the volume of the water in the pool when it is full.

Answer 1

4500 m³

Explanation:

The surface of a swimming pool is 50-meter long and 20-meter wide rectangle. The pool is 1 meter deep at the shallow end and 8 meters deep at the other end.

The pool can be divided into two sections, the first section (top) is a rectangular prism which sits on top of the bottom section. The second section (bottom) is a triangular prism sits below the top section.

The rectangular prism has a length of 50 m, width of 20 m and a height of 1 m.

The volume of a rectangular prism = length × width × height = 50 × 20 × 1 = 1000 m³

The triangular prism has a base of 50 m, length of 20 m and a height of 8 m - 1 m = 7 m.

The volume of a triangular prism = 1/2 × base × length × height = 1/2 × 50 × 20 × 7 = 3500 m³

The volume of water in the pool = volume of a rectangular prism + volume of a triangular prism = 1000 m³ + 3500 m³ = 4500 m³

Answer 2

V = 4500 m³

Explanation:

The cross section of the swimming pool is a trapezium with parallel sides 1m and 8m (depth of both ends) and 50m (length of pool) as the perpendicular distance between the parallel sides.

The width of pool 1m can be the length of cross section.

Length of swimming pool = 50m

Breadth of the pool = 20m

Depth of the pool=1m and 8m

Let's assume it slopes uniformly, thus;

Volume of water when full;

V = ½[(1 + 8) × 50] × 20 = 25 × 9 × 20

V = 4500 m³