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 given by the formula V = base area x height. Since the base of the prism is a triangle with height 15 m, the base area is 1/2 x base x height = 1/2 x base x 15.
The volume of the prism is then V = (1/2 x base x 15) x 15 = 7.5 x base x 15 = 112.5 x base.
The volume of a pyramid is given by the formula V = 1/3 x base area x height. Since the base of the pyramid is a triangle with height 15 m, the base area is 1/2 x base x height = 1/2 x base x 15.
The volume of the pyramid is then V = (1/3 x 1/2 x base x 15) x 15 = 7.5 x base x 15 x 1/3 = 37.5 x base.
Since the two shapes have congruent bases, their volumes are proportional to the base areas. Therefore, the volume of the prism is 2.5 times the volume of the pyramid.
Since the volume of the prism is  m^3, the volume of the pyramid is  m^3.