Question

Use the model for the base of a triangular, prism and a triangular pyramid. If the heights are both 9 cm, what is the volume of each shape

Answer 1

To find the volume of each shape, we first need to calculate the area of the base of each shape.

1. Base of the triangular prism:
The base of the triangular prism is a triangle. We can use the formula for the area of a triangle: A = 1/2 * base * height
Given that the base and height of the triangle are 9 cm each, we get:
A = 1/2 * 9 cm * 9 cm = 40.5 cm^2

2. Base of the triangular pyramid:
The base of the triangular pyramid is also a triangle, so we can use the same formula: A = 1/2 * base * height
Given that the base and height of the triangle are 9 cm each, we get:
A = 1/2 * 9 cm * 9 cm = 40.5 cm^2

Now that we have the areas of the bases, we can calculate the volumes of each shape.

3. Volume of the triangular prism:
The volume of a prism is given by the formula: V = base area * height
Given that the base area is 40.5 cm^2 and the height is 9 cm, we get:
V = 40.5 cm^2 * 9 cm = 364.5 cm^3

4. Volume of the triangular pyramid:
The volume of a pyramid is given by the formula: V = 1/3 * base area * height
Given that the base area is 40.5 cm^2 and the height is 9 cm, we get:
V = 1/3 * 40.5 cm^2 * 9 cm = 121.5 cm^3

Therefore, the volume of the triangular prism is 364.5 cm^3 and the volume of the triangular pyramid is 121.5 cm^3.