Use the image to answer the question.
COURSE TOOLS
: 4 cm
Item 1
Item 2
• Item 3.
Item 4
Item 5
6 cm
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)
• prism: 72 cm"; pyramid: 216 cm' O prism: 216 cm"; pyramid: 72 cmg O prism: 36 cm'; pyramid: 108 cm'
• prism: 108 cm'; pyramid: 36 cm?
The volume of a triangular prism is given by V = (1/2) * base * height, and the volume of a triangular pyramid is given by V = (1/3) * (1/2) * base * height.
For the prism:
V = (1/2) * 4 cm * 9 cm
V = 18 cm^2
For the pyramid:
V = (1/3) * (1/2) * 4 cm * 9 cm
V = 6 cm^2
Therefore, the correct answer is:
- Prism: 72 cm^3
- Pyramid: 24 cm^3
height is 4cm
Thank you for pointing that out. Given that the height of both the prism and the pyramid is 4 cm, the calculations would be as follows:
For the prism:
V = (1/2) * 4 cm * 4 cm * 9 cm
V = 72 cm^3
For the pyramid:
V = (1/3) * (1/2) * 4 cm * 4 cm * 9 cm
V = 24 cm^3
Therefore, the correct answer is:
- Prism: 72 cm^3
- Pyramid: 24 cm^3
bottom is 6 cm
Thank you for the correction. Given that the base of the triangular prism and the triangular pyramid is 6 cm, and the height for both shapes is 4 cm:
For the prism:
V = base * height * height of prism = 6 cm * 4 cm * 9 cm = 216 cm^3
For the pyramid:
V = (1/3) * base * height * height of pyramid = (1/3) * 6 cm * 4 cm * 9 cm = 72 cm^3
Therefore, the volume of each shape is:
- Triangular prism: 216 cm^3
- Triangular pyramid: 72 cm^3