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?
The triangular prism has a larger volume than the triangular pyramid.
To find the volume of the pyramid, we use the formula: V = (1/3) * base area * height = (1/3) * (1/2) * base * height = (1/6) * 3 * 5 * 8.41 = 21.08 in^3
To find the volume of the prism, we use the formula: V = base area * height = (1/2) * base * height = (1/2) * 3 * 5 * 8.41 = 63.24 in^3
The difference in volume is 63.24 - 21.08 = 42.16 in^3, so the prism has a volume that is 42.16 in^3 larger than the pyramid.