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: 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 prism: 108 cm cubed ; pyramid: 36 cm cubed prism: 216 cm3; pyramid: 72 cm3
prism: 36 cm cubed ; pyramid: 108 cm cubed
To find the volume of a triangular prism, you use the formula: V = Bh, where B is the area of the base and h is the height. In this case, the base is a triangle with a base of 6 cm and height of 9 cm. So, the area of the base is 1/2 * 6 * 9 = 27 cm². Therefore, the volume of the prism is 27 cm² * 9 cm = 243 cm³.
To find the volume of a triangular pyramid, you also use the formula: V = 1/3Bh, where B is the area of the base and h is the height. In this case, the base is the same triangle with an area of 27 cm². Therefore, the volume of the pyramid is 1/3 * 27 cm² * 9 cm = 81 cm³.