Question

A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 600 ft.3 , what is the volume of the pyramid?

height = 6ft

base = 20ft

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a prism is given by the formula V = Bh, where B is the base area and h is the height.

Since both the prism and the pyramid have the same height and base, their volumes are directly proportional to the area of their bases.

The formula for the volume of a pyramid is V = (1/3)Bh, where B is the base area and h is the height.

Since the base of both the prism and the pyramid is a triangle, the base area is given by B = (1/2)bh, where b is the base and h is the height.

Given that the base of the prism is 20ft and the height is 6ft, the base area is B = (1/2)(20)(6) = 60 ft^2.

Therefore, the volume of the pyramid is V = (1/3)(60)(6) = 120 ft^3.