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 numbers of the shape are 14, 7, 8, 16
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 prism and pyramid have congruent triangular bases, their bases have the same area. The area of a triangle is given by the formula A = 1/2 * base * height.
Since the height of both the prism and pyramid is 15m, the area of the bases is the same for both shapes.
Let's assume the base of each shape has measurements base = b and height = h. Then, the area of the base for both shapes is A = 1/2 * b * h.
The volume of the prism will be V_prism = Bh = (1/2bh) * 15 = 7.5bh.
The volume of the pyramid will be V_pyramid = (1/3)Bh = (1/3) * (1/2bh) * 15 = 2.5bh.
Therefore, the volume of the prism is 7.5bh and the volume of the pyramid is 2.5bh.