B. The prism has a larger volume by three times.
To calculate the volume of a triangular pyramid, we use the formula V = 1/3 * base area * height. The base area of the triangular pyramid is (1/2) * base * height = (1/2) * 5 * 8.41 = 21.025 square inches. Therefore, the volume of the pyramid is V = 1/3 * 21.025 * 8.41 = 59.206 cubic inches.
To calculate the volume of a triangular prism, we use the formula V = base area * height. The base area of the triangular prism is (1/2) * base * height = (1/2) * 5 * 8.41 = 21.025 square inches. Therefore, the volume of the prism is V = 21.025 * 8.41 = 176.687 cubic inches.
The prism has a larger volume by 176.687 / 59.206 = 2.987 times, which is approximately three times.
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
Por favorrrr
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