Use the model for the base of a triangular prism and triangular pyramid. If the heights are both 9 cm, what is the volume of each shape?
4 cm
6 cm
The volume of a prism is calculated using the formula V = Bh, where B is the area of the base and h is the height.
Triangular prism:
The base of the triangular prism is a triangle with a base of 4 cm and a height of 6 cm. Therefore, the area of the base is (1/2) x 4 x 6 = 12 cm^2.
The volume of the triangular prism is V = 12 x 9 = 108 cm^3.
Triangular pyramid:
The base of the triangular pyramid is also a triangle with a base of 4 cm and a height of 6 cm. Therefore, the area of the base is also 12 cm^2.
The volume of the triangular pyramid is V = (1/3) x 12 x 9 = 36 cm^3.