A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?
14m 7m 8m 16m
(1 point)
The volume of the prism is m3.
The volume of the pyramid is m3.
The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. Since the triangular base of the prism is congruent to the triangular base of the pyramid, their areas will be the same. The area of a triangle with base b and height h is given by A = 0.5 * base * height.
In this case, the base of the triangle is 14 m and the height is 7 m. So, the area of the base is A = 0.5 * 14 * 7 = 49 m^2.
Therefore, the volume of the prism and the pyramid will be the same since they have the same base area and height.
Volume of prism = (49 m^2) * 15 m = 735 m^3
Volume of pyramid = (49 m^2) * 15 m * 1/3 = 245 m^3
So, the volume of the prism is 735 m^3 and the volume of the pyramid is 245 m^3.
Wrong answer
I apologize for the mistake.
Given that the triangular bases of the prism and pyramid are congruent, we can calculate the area of the base triangle using the formula A = 0.5 * base * height.
Area of the base triangle = 0.5 * 14 * 7 = 49 square meters
For the prism:
Volume = Base Area * Height = 49 * 15 = 735 cubic meters
For the pyramid:
Volume = (1/3) * Base Area * Height = (1/3) * 49 * 15 = 245 cubic meters
Therefore, the volume of the prism is 735 cubic meters and the volume of the pyramid is 245 cubic meters.