The pyramid is 6 cm and 4 cm 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)
• prism: 36 cm³ pyramid: 108 cm ³
• prism: 216 cm³ pyramid: 72 cm ³
• prism: 72 cm³ pyramid. 216 cm ³
• prism: 108 cm³ pyramid: 36 cm ³
To calculate 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.
The base of the triangular prism is the triangle with sides of 6 cm and 4 cm. Using the formula for the area of a triangle (A = 1/2 * base * height), we find that the base area is 1/2 * 6 cm * 4 cm = 12 cm².
Therefore, the volume of the triangular prism is V = 12 cm² * 9 cm = 108 cm³.
To calculate the volume of a triangular pyramid, you use the formula V = 1/3 * Bh, where B is the area of the base and h is the height.
The base of the triangular pyramid is the same triangle with sides of length 6 cm and 4 cm. The base area is 12 cm². Therefore, the volume of the triangular pyramid is V = 1/3 * 12 cm² * 9 cm = 36 cm³.
So the correct answer is:
• prism: 108 cm³ pyramid: 36 cm ³.