A swimming pool is 6m wide by 12m long, with depths of 1.20m at one end and 2.40m at the other. How many gallons of water does it contain?

To determine the volume of water in the swimming pool, you can use the formula for the volume of a trapezoidal prism, as the pool has a varying depth. The formula is given by:

[ V = \text{Area of the base} \times \text{Height} ]

In this case, the base area is a trapezoid, and the volume can be found by calculating the average depth of the pool, multiplying this by the surface area.

1. Calculate the surface area of the pool:

The surface area is calculated by multiplying the width and the length.

[ \text{Surface area} = 6 \text{ m} \times 12 \text{ m} = 72 \text{ m}^2 ]

2. Calculate the average depth:

The average depth of the pool is calculated by taking the sum of the two depths and dividing by 2.

[ \text{Average depth} = \frac{1.20 \text{ m} + 2.40 \text{ m}}{2} = \frac{3.60 \text{ m}}{2} = 1.80 \text{ m}