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A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 1,092 cubic units, what is the volume of the pyramid?
(1 point)
• 1,092 cubic units
• 3,276 cubic units
• 364 cubic units
O 728 cubic units
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To find the volume of the pyramid, we need to use the formula for the volume of a pyramid, which is V = (1/3) * base area * height.
Since both the prism and the pyramid have the same base and height, and the prism has a volume of 1,092 cubic units, we can use the formula for the volume of a prism to find the base area of the triangular base.
Volume of prism = base area * height
1,092 = base area * height
Since the base and height are the same for both the prism and the pyramid, the base area for the pyramid is the same as the base area for the prism, which is 1,092.
Now we can find the volume of the pyramid using the formula for the volume of a pyramid:
V = (1/3) * base area * height
V = (1/3) * 1,092 * 10
V = 3,276 cubic units
Therefore, the volume of the pyramid is 3,276 cubic units. The answer is B.