Questions: Find the volume of this composite figure: (Note: A triangular prism is half of a rectangular prism.) A 272.1 m^3 B 472.5 m^3 C 475.5 m^3 D 675.0 m^3

Solution Steps

The triangular prism's volume is given by the formula \(V = \frac{1}{2} \times \text{base} \times \text{height} \times \text{length}\). In our case, the base of the triangle is 9 m, the height is 15 m, and the length of the prism is 5 m. So, the volume of the triangular prism is \(V = \frac{1}{2} \times 9 \text{ m} \times 15 \text{ m} \times 5 \text{ m} = 337.5 \text{ m}^3\).

The rectangular prism's volume is given by the formula \(V = \text{length} \times \text{width} \times \text{height}\). Here, the length is 5 m, the width is 6 m, and the height is 15 m - 9 m = 6 m. This means the height is only the part that is not covered by the triangular prism. So, the volume of the rectangular prism is \(V = 5 \text{ m} \times 6 \text{ m} \times (15-9) \text{ m} = 5 \text{ m} \times 6 \text{ m} \times 6 \text{ m} = 180 \text{ m}^3\).

The total volume of the composite figure is the sum of the volumes of the triangular prism and the rectangular prism. Total volume \(= 337.5 \text{ m}^3 + 180 \text{ m}^3 = 517.5 \text{ m}^3\).

Final Answer