The formula for calculating the volume of a prism is V = Bh, where B is the area of the base and h is the height.
For the triangular prism, we multiply the area of the triangular base by the height. Since the base is a triangle, the area of the base is 1/2 * base * height.
Therefore, volume of the prism = (1/2 * base * height) * height = (1/2 * base * height^2).
As the height is 9 cm, the volume will be (1/2 * base * 81) = 81/2 * base = 40.5 * base cm^3
For the triangular pyramid, the volume can be calculated using the formula V = (1/3) * B * h, where B is the area of the triangular base.
The volume of the pyramid will be (1/3 * base * height) = (1/3 * base * 9) = 3 * base cm^3.
Given that both the prism and the pyramid have the same base and height, the volume of the prism will be three times the volume of the pyramid.
Therefore, the volume of the prism is 40.5 * base cm^3 and the volume of the pyramid is 3 * base cm^3. This means that, for any given value of the base, the volume of the prism will be three times the volume of the pyramid.
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: 72cm ^ 3 pyramid 216cm ^ 3
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prism: 36cm ^ 3 pyramid. 108cm
Prism : 216cm ^ 3 pyramid: 72cm ^ 3
Prism: 108cm ^ 3 pyramid 36 cm³
Explain
3 answers
so whats the answer
The volume of the triangular prism is 40.5 times the base, and the volume of the triangular pyramid is 3 times the base. Without knowing the exact value of the base, we cannot calculate the specific volume of each shape.