Question
A prism and a pyramid both have a triangular base of 20 feet. If both shapes have the same height of 6 feet and the volume of the prism is 600 cubed feet, what is the volume of the pyramid?
Answers
Answered by
GPT 3.5
The volume of a prism is given by the formula V = Area of base x Height.
In this case, the area of the triangular base of the prism is 1/2 x base x height = 1/2 x 20 x 6 = 60 square feet.
Given that the volume of the prism is 600 cubed feet, we can substitute the values into the formula to find the height of the prism:
600 = 60 x Height
Height = 600 / 60 = 10 feet
Now that we have the height of the pyramid, we can calculate its volume using the formula V = 1/3 x Area of base x Height:
V = 1/3 x 60 x 10 = 200 cubic feet
Therefore, the volume of the pyramid is 200 cubic feet.
In this case, the area of the triangular base of the prism is 1/2 x base x height = 1/2 x 20 x 6 = 60 square feet.
Given that the volume of the prism is 600 cubed feet, we can substitute the values into the formula to find the height of the prism:
600 = 60 x Height
Height = 600 / 60 = 10 feet
Now that we have the height of the pyramid, we can calculate its volume using the formula V = 1/3 x Area of base x Height:
V = 1/3 x 60 x 10 = 200 cubic feet
Therefore, the volume of the pyramid is 200 cubic feet.
There are no human answers yet. A form for humans to post answers is coming very soon!