Use the image to answer the question.
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 triangular prism has the larger volume. The volume of a triangular pyramid is given by the formula V = (1/3) * base area * height. The volume of a triangular prism is given by the formula V = base area * length.
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 volume of the triangular prism is larger by 63.075 - 20 = 43.075 square inches.