A prism and pyramid have congruent triangular bases. If their heights are both 15m. What is the volume of each
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 base of the prism is a triangle and its area is given by A = 1/2bh, where b is the base length and h is the height, the volume of the prism can be calculated as follows:
V_prism = (1/2bh) * 15 = (1/2 * b * 15) * 15 = 7.5b * 15 = 112.5b
Similarly, 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 a triangle and its area is given by A = 1/2bh, the volume of the pyramid can be calculated as follows:
V_pyramid = (1/3 * 1/2bh) * 15 = (1/6 * b * 15) * 15 = 2.5b * 15 = 37.5b
Therefore, the volume of the prism is 112.5b cubic meters and the volume of the pyramid is 37.5b cubic meters, where b is the base length of the triangle.