An illustration shows a triangular pyramid and a triangular prism. The edges that are not visible are marked as dashed lines. The triangular pyramid has the triangular face as its base. The sides of of the triangular base measure 3 inches and 5 inches. The perpendicular height of the pyramid is 8.41 inches. The triangular prism has its triangular face as the base. The sides of the triangular base measure 3 inches and 5 inches. The length of the side is 8.41 inches.
Which shape has the larger volume? How much larger is it?
A. The volumes are the same.
B. The prism has a larger volume by three times.
C. The prism has a larger volume by 1/3 times.
D. The pyramid has a larger volume by three times
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C. The prism has a larger volume by 1/3 times.
To calculate the volume of a pyramid, you use the formula V = (1/3) * base area * height.
For the triangular pyramid, the base area is (1/2) * 3 * 5 = 7.5 square inches.
So, the volume of the pyramid is V = (1/3) * 7.5 * 8.41 = 20.025 cubic inches.
To calculate the volume of a prism, you use the formula V = base area * height.
For the triangular prism, the base area is (1/2) * 3 * 5 = 7.5 square inches.
So, the volume of the prism is V = 7.5 * 8.41 = 63.075 cubic inches.
The prism has a larger volume by 63.075 - 20.025 = 43.05 cubic inches.
To verify how many times larger the prism is, we divide 63.075 by 20.025, which equals approximately 3.15.
Therefore, the prism has a larger volume by approximately 1/3 times.