Use the image to answer the question. Use the model for the base of a triangular prism and triangular pyramid. If the heights are both 9 cm, what is the volume of each shape? (1 point) Responses prism: 216 cm3; pyramid: 72 cm3 prism: 216 cm cubed ; pyramid: 72 cm cubed prism: 36 cm3; pyramid: 108 cm3 prism: 36 cm cubed ; pyramid: 108 cm cubed prism: 72 cm3; pyramid: 216 cm3 prism: 72 cm cubed ; pyramid: 216 cm cubed prism: 108 cm3; pyramid: 36 cm3
To find the volume of a triangular prism, we use the formula V = 1/2 * base area * height. The base area of the model is a triangle with base 6 cm and height 6 cm, so the base area is 1/2 * 6 * 6 = 18 cm^2.
Therefore, the volume of the triangular prism is V = 1/2 * 18 * 9 = 81 cm^3.
To find the volume of a triangular pyramid, we use the formula V = 1/6 * base area * height.
Therefore, the volume of the triangular pyramid is V = 1/6 * 18 * 9 = 27 cm^3.
Therefore, the correct answer is prism: 81 cm^3; pyramid: 27 cm^3.