An illustration shows a triangle with its base as 20 feet and its perpendicular height as 6 feet.
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?
600 ft.3
200 ft.3
400 ft.3
1,800 ft.3
400 ft.3
The volume of a prism is given by V = Bh, where B is the base area and h is the height. Since the triangle is the base of both the prism and the pyramid, the base area will be the same for both shapes.
Given that the volume of the prism is 600 ft.3 and the height is the same for both shapes, the volume of the pyramid will be 1/3 of the volume of the prism, as the volume of a pyramid is 1/3 of a prism with the same base and height.
Therefore, the volume of the pyramid will be 1/3 of 600 ft.3, which is 200 ft.3.
you sure
Apologies for the mistake in my previous response.
Let's reevaluate the problem:
Since the base of both the prism and the pyramid is a triangle with base 20 ft and height 6 ft, the volume formula for a prism is V = Bh = 20 * 6 * h = 120h.
Given that the volume of the prism is 600 ft.3, we have:
120h = 600
h = 600 / 120
h = 5 ft
So, the height of both the prism and the pyramid is 5 ft.
Now, the volume of the pyramid will be 1/3 of the volume of the prism, as the volume of a pyramid is 1/3 of a prism with the same base and height. Therefore, the volume of the pyramid will be:
V_pyramid = 1/3 * 600 ft.3 = 200 ft.3
Therefore, the correct answer is 200 ft.3.