The volume of a triangular prism is given by the formula V = base area x height. The volume of a triangular pyramid is given by the formula V = (1/3) x base area x height.
Since the base of both shapes is the same, we only need to determine the base area in order to find the volume of the shapes.
The formula for the area of a triangle is A = (1/2) x base x height.
Given that the base of both shapes is a triangle with a base of 12 cm and height of 9 cm:
Area = (1/2) x 12 cm x 9 cm = 54 cm²
Therefore, the volume of the triangular prism is V = 54 cm² x 9 cm = 486 cm³, and the volume of the triangular pyramid is V = (1/3) x 54 cm² x 9 cm = 162 cm³.
So the correct answer is:
prism: 486 cm³; pyramid: 162 cm³.
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)
O prism: 216 cm?. pyramid: 72 cm3
O prism: 108 cm?: pyramid: 36 cm°
O prism: 72 cm°: pyramid: 216 cm?
O prism: 36 cm°; pyramid: 108 cm?
1 answer