A 15 meter long cylinder with a diameter of 7 meters has a square prism with a base length of 4 meters hole going all the way through the center of
it as shown in the diagram (not to scale). Find the volume of the composite
shape rounding to the nearest cubic meter.

The volume of the composite figure is approximately 337.27 m³

Step-by-step explanation:

The given parameters are;

The length of the cylinder, L = 15 meters

The diameter of the cylinder, D = 7 meters

The base length of the square prism, B = 4 meters

We note that the square diagonal of the square = √(4² + 4²) = 4·√2 ≈ 5.66 meters, fits in the cylinder

Therefore, we have;

The volume of the composite figure = The volume of the cylinder - The volume of the square prism

The volume of the cylinder = π/4 × D² × L = π/4 × 7² × 15 ≈ 577.27 m³

The volume of the square prism = B² × L = 4² × 15 = 240 m³

∴ The volume of the composite figure ≈ 577.27 m³ - 240 m³ ≈ 337.27 m³

The volume of the composite figure ≈ 337.27 m³.