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 = Bh, where B is the area of the base and h is the height. The base of the prism is a triangle with base and height equal to 15 meters each. Therefore, the area of the base is:
B = 1/2 * base * height
B = 1/2 * 15 * 15
B = 112.5 m^2
Now, plug the values of B and h into the formula for the volume of a prism:
V = Bh
V = 112.5 * 15
V = 1687.5 m^3
Therefore, the volume of the prism is 1687.5 m^3.
The volume of a pyramid is given by the formula V = (1/3) * Bh, where B is the area of the base and h is the height. Since the base of the pyramid is also a triangle with base and height equal to 15 meters each, the area of the base is the same as for the prism: 112.5 m^2.
Now, plug the values of B and h into the formula for the volume of a pyramid:
V = (1/3) * 112.5 * 15
V = 562.5 m^3
Therefore, the volume of the pyramid is 562.5 m^3.