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?
(1 point)
Responses
The pyramid has a larger volume by three times.
The pyramid has a larger volume by three times.
The prism has a larger volume by 13 times.
The prism has a larger volume by Start Fraction 1 over 3 End Fraction times.
The prism has a larger volume by three times.
The prism has a larger volume by three times.
The volumes are the same.
The volumes are the same.
The pyramid has a larger volume. The volume of a pyramid is given by V = (1/3) * base area * height. The base area of the pyramid is (1/2) * 3 * 5 = 7.5 square inches. So, the volume of the pyramid is V = (1/3) * 7.5 *8.41 = 20 cubic inches.
The volume of a prism is given by V = base area * height. The base area of the prism is 7.5 square inches. So, the volume of the prism is V = 7.5 * 8.41 = 63.075 cubic inches.
Therefore, the pyramid has a larger volume by 42.575 cubic inches.