A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape? 14cm 16cm 7cm 8cm
To calculate the volume of a prism, you use 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, the area is given by the formula A = (1/2)bh, where b is the base length and h is the height of the triangle.
Given that the height is 15m and the base is congruent to the base of the pyramid, which is not given, let's use the given options for the base length:
Option 1: b = 14 cm
Base area = (1/2)(14 cm)(15 m) = 105 cm^2 = 0.0105 m^2
Volume of prism = (0.0105 m^2)(15 m) = 0.1575 m^3
Option 2: b = 16 cm
Base area = (1/2)(16 cm)(15 m) = 120 cm^2 = 0.0120 m^2
Volume of prism = (0.0120 m^2)(15 m) = 0.180 m^3
Option 3: b = 7 cm
Base area = (1/2)(7 cm)(15 m) = 52.5 cm^2 = 0.00525 m^2
Volume of prism = (0.00525 m^2)(15 m) = 0.07875 m^3
Option 4: b = 8 cm
Base area = (1/2)(8 cm)(15 m) = 60 cm^2 = 0.0060 m^2
Volume of prism = (0.0060 m^2)(15 m) = 0.09 m^3
Therefore, the volume of the prism depends on the base length which is not provided.