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)
The volume of a pyramid is given by the formula V = (1/3) * base area * height. The volume of a pyramid is V = (1/3) * (1/2) * (5 * 3) * 8.41 = 42.05 cubic inches.
The volume of a prism is given by the formula V = base area * height. The volume of a prism is V = (1/2) * (5 * 3) * 8.41 = 63.15 cubic inches.
Therefore, the triangular prism has the larger volume, by 21.1 cubic inches.