A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape? (1 point)
The volume of the prism is __m3.
The volume of the pyramid is __m3.
The volume of a prism is equal to the area of the base times the height, so V_prism = 1/2 * b * 15, where b is the area of the triangular base of the prism.
The volume of a pyramid is equal to 1/3 times the area of the base times the height, so V_pyramid = 1/6 * b * 15, where b is the area of the triangular base of the pyramid.
Since the bases of the prism and pyramid are congruent triangles, their areas are the same.
Thus,
V_prism = 1/2 * b * 15 = 1/2 * V_pyramid = 1/6 * b * 15
=> b * 15 = 1/3 * b * 15
=> b = 1/3 * b
Therefore, the volume of the prism is 7.5m3 and the volume of the pyramid is 2.5m3.