Question

A rectangular swimming pool is 50 meters long and 25 meters wide. Its depth is always the same along its width but linearly increases along its length from 1 meter at one end to 4 meters at the other end. How much water (in cubic meters) is needed to completely fill the pool?

• A. 2500
• B. 3125
• C. 3750
• D. 1875
• E. 1250

Answer 1

The Correct Option is B

To calculate the volume of water needed to fill the pool, we need to consider the pool's unique depth profile. The depth increases linearly from 1 meter to 4 meters along its 50-meter length. This means the pool's depth can be modeled as a trapezoidal prism.

The formula for the volume \( V \) of a trapezoidal prism is:

\( V = \text{Area of base} \times \text{Width} \)

Where the base is a trapezoid with the following characteristics:

• Base 1 (\( a \)) = 1 meter (depth at one end)
• Base 2 (\( b \)) = 4 meters (depth at the other end)
• Height (\( h \)) = 50 meters (length of the pool)

The area of the trapezoid is calculated using:

\( \text{Area} = \frac{1}{2} \times (a+b) \times h \)

\( \text{Area} = \frac{1}{2} \times (1+4) \times 50 \)

\( \text{Area} = \frac{1}{2} \times 5 \times 50 \)

\( \text{Area} = 2.5 \times 50 \)

\( \text{Area} = 125 \text{ square meters} \)

The width of the pool is 25 meters. Thus, the volume is:

\( V = 125 \times 25 \)

\( V = 3125 \text{ cubic meters} \)

Therefore, 3125 cubic meters of water are needed to completely fill the pool.