If the heights of a triangular prism and triangular pyramid are both 9 cm what is the volume of each shape
To calculate the volume of a triangular prism, the formula is:
Volume = Base area x Height
First, we need to find the base area of the triangular prism. Since it is a triangle, we can use the formula for the area of a triangle:
Base area = (1/2) x base x height of the triangle
Assuming the base of the triangle is 6 cm, the base area = (1/2) x 6 x 9 = 27 cm^2
Now, we can calculate the volume of the triangular prism:
Volume = 27 cm^2 x 9 cm = 243 cm^3
To calculate the volume of a triangular pyramid, the formula is:
Volume = (1/3) x Base area x Height
Since we already calculated the base area of the triangle in the triangular prism above as 27 cm^2, we can use that value.
Volume = (1/3) x 27 cm^2 x 9 cm = 81 cm^3
Therefore, the volume of the triangular prism is 243 cm^3 and the volume of the triangular pyramid is 81 cm^3.