A prism and a pyramid both have this triangular base. If both shapes have the height and the volume of the prism is 540 inches cubed what is the volume of the pyramid?
5 inches long
10 inches width
To find the volume of the pyramid, we first need to calculate the area of the triangular base. Since the base of both the prism and the pyramid are the same, we can first find the area of the base.
The area of a triangle is given by the formula:
Area = (1/2) * base * height
In this case, the base is 10 inches and the height is 5 inches. Plugging these values into the formula:
Area = (1/2) * 10 * 5
Area = 25 square inches
Now that we have the area of the base, we can find the volume of the pyramid. The volume of a pyramid is given by the formula:
Volume = (1/3) * base area * height
In this case, the base area is 25 square inches and the height is also 5 inches. Plugging these values into the formula:
Volume = (1/3) * 25 * 5
Volume = 41.67 inches cubed
Therefore, the volume of the pyramid is 41.67 inches cubed.