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?
(1 point)
O prism: 72c * m ^ 3 pyramid: 216c * m ^ 3
O prism: 108 c * m ^ 3 pyramid: 36c * m ^ 3
O prism: 216c * m ^ 3 pyramid: 72c * m ^ 3
O prism: 36c * m ^ 3 pyramid: 108c * m ^ 3
O prism: 72cm^3 pyramid: 36cm^3
To find the volumes of the shapes, we use the formula:
Volume of Prism = (1/2) * base area * height
Volume of Pyramid = (1/3) * base area * height
Since the base is a triangle, we need to find its area first. The formula for the area of a triangle is:
Area of Triangle = (1/2) * base * height
Given that the base is 8 cm and the height is 9 cm:
Area of Triangle = (1/2) * 8 cm * 9 cm = 36 cm^2
Now, we can find the volumes of the prism and pyramid:
Volume of Prism = (1/2) * 36 cm^2 * 9 cm = 162 cm^3
Volume of Pyramid = (1/3) * 36 cm^2 * 9 cm = 108 cm^3
Therefore, the volume of the prism is 162 cm^3 and the volume of the pyramid is 108 cm^3.