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 cm ; pyramid: 3 108 cm3
prism: 216 cm ; pyramid: 3 72 cm3
prism: 108 cm ; pyramid: 3 36 cm3
prism: 72 cm ; pyramid: 3 216 cm
The volume of a prism is given by the formula V = (1/2) * b * h, where b is the area of the base and h is the height. The volume of a pyramid is given by the formula V = (1/3) * b * h.
Since the base of both the prism and pyramid is a triangle, the area of the base can be calculated using the formula for the area of a triangle: A = (1/2) * b * h.
Given that the height is 9 cm, we can calculate the area of the base of the prism and pyramid:
Base area = (1/2) * 9 * 6 = 27 cm^2
Now, we can calculate the volume of the prism and pyramid using the formulas mentioned above:
Prism volume = (1/2) * 27 * 9 = 121.5 cm^3
Pyramid volume = (1/3) * 27 * 9 = 81 cm^3
Therefore, the correct answer is:
prism: 121.5 cm3; pyramid: 81 cm3