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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D. The pyramid has a larger volume by three times.
To calculate the volume of the triangular pyramid, we use the formula V = (1/3) * base area * height. The base area of the triangular pyramid is (1/2) * 3 * 8.41 = 12.615 square inches. Therefore, the volume of the pyramid is V = (1/3) * 12.615 * 8.41 = 33.71 cubic inches.
To calculate the volume of the triangular prism, we use the formula V = base area * height. The base area of the triangular prism is (1/2) * 3 * 8.41 = 12.615 square inches. Therefore, the volume of the prism is V = 12.615 * 8.41 = 106 cubic inches.
The pyramid has a volume of 33.71 cubic inches, while the prism has a volume of 106 cubic inches. The prism has a larger volume by three times.