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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The volume of a pyramid is given by the formula V = (1/3) * base area * height, while the volume of a prism is given by the formula V = base area * height.
For the triangular pyramid:
Base area = (1/2) * 3 * 5 = 7.5 square inches
Volume = (1/3) * 7.5 * 8.41 = 20 square inches
For the triangular prism:
Base area = (1/2) * 3 * 5 = 7.5 square inches
Volume = 7.5 * 8.41 = 63.075 square inches
Therefore, the prism has a larger volume. The volume of the prism is 63.075 - 20 = 43.075 square inches larger than the volume of the pyramid.
So, the answer is:
C. The prism has a larger volume by approximately 3 times.