Find the volume in cubic metres of a cylindrical tank that is 6 m in diameter and 12 m long.

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

[ V = \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius of the cylinder, and ( h ) is the height (or length) of the cylinder.

In this case, the diameter of the tank is 6 m, which means the radius ( r ) is half of the diameter:

[ r = \frac{6}{2} = 3 , \text{m} ]

The length ( h ) of the tank is given as 12 m.

Now, substituting the values into the volume formula:

[ V = \pi (3)^2 (12) ]

[ V = \pi (9)(12) ]

[ V = \pi (108) ]

[ V \approx 3.14159 \times 108 ]

[ V \approx 339.292 , \text{m}^3 ]

When rounded off, the volume is approximately 339.293 cubic metres. This matches the choice that was selected.

The calculation reflects the correct assessment of the cylindrical volume, utilizing the radius derived from the