Questions
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?
pls and ty
To find the volume of the pyramid, we first need to find the area of the triangular base.
The area of a triangle is calculated using the formula: 1/2 x base x height
In this case, the base is 20 feet and the height is 6 feet.
Area = 1/2 x 20 x 6 = 60 ft²
Since the prism and the pyramid both have the same height, the volume of the triangular prism with base area 60 ft² and volume 600 ft³ can be calculated as follows:
Volume = base area x height
600 ft³ = 60 ft² x height
height = 600 ft³ / 60 ft²
height = 10 feet
Now, we can calculate the volume of the pyramid using the formula for the volume of a pyramid, which is 1/3 x base area x height.
Volume of the pyramid = 1/3 x 60 ft² x 10 ft
Volume of the pyramid = 200 ft³
Therefore, the volume of the pyramid is 200 ft³.