The volume of a triangular prism is 90. Find the volume of a triangular pyramid
| January 31, 2021 | education
The volume of a triangular prism is 90. Find the volume of a triangular pyramid with the same base and height, 2 times less than that of the prism.
Triangular prism volume:
V = S * h, where S is the area of the base of the prism, h is the height of the prism.
Volume of a triangular pyramid:
V1 = 1/3 * S1 * h1, where S1 is the area of the base of the pyramid (S1 = S), h1 is the height of the pyramid (h1 = 0.5h).
V1 = 1/3 * S1 * h1 = 1/3 * S * 0.5h = 1/6 S * h.
The ratio of the volume of the prism to the volume of the pyramid: V / V1 = S * h / (1/6 S * h) = 1 / 1/6 = 6.
Since the volume of the prism is 6 times larger, the volume of the pyramid is: V1 = V / 6 = 90/6 = 15.
Answer: The volume of a triangular pyramid is 15.
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