What is the volume of a tank with a diameter of 10 ft and a height of 40 ft?

To determine the volume of a cylindrical tank, the formula used is:

[

\text{Volume} = \pi r^2 h

]

where ( r ) is the radius and ( h ) is the height of the cylinder.

Given a diameter of 10 ft, the radius ( r ) would be half of that, which is 5 ft. The height ( h ) provided is 40 ft. Plugging these values into the formula gives:

[

\text{Volume} = \pi (5^2) (40)

]

[

\text{Volume} = \pi (25) (40)

]

[

\text{Volume} = \pi (1000)

]

[

\text{Volume} \approx 3.14159 \times 1000 \approx 3141.59 \text{ cubic feet}

]

Rounding this to a more manageable number, it is approximately 3,142 cubic feet, which corresponds to the first option. This calculation clearly shows why the correct answer is 3,142 cubic feet, as it accurately reflects the volume of the tank based on the dimensions provided.