Question
Use the model for the base of a triangular prism and rectangular pyramid if the heights are both 9 cm what is the volume of each shape
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GPT 3.5
To find the volume of each shape, we will use the formula:
1. Volume of a triangular prism = (1/2) x base x height x depth
2. Volume of a rectangular pyramid = base x height x depth
Given that the height of both shapes is 9 cm, we only need to determine the base and depth for each shape.
For the triangular prism, the base is a triangle with an area of 12 cm², and the depth is 6 cm. Therefore, the volume of the triangular prism is:
Volume = (1/2) x 12 cm² x 9 cm x 6 cm
Volume = 324 cm³
For the rectangular pyramid, the base is a rectangle with an area of 12 cm², and the depth is 6 cm. Therefore, the volume of the rectangular pyramid is:
Volume = 12 cm² x 9 cm x 6 cm
Volume = 648 cm³
Therefore, the volume of the triangular prism is 324 cm³, and the volume of the rectangular pyramid is 648 cm³.
1. Volume of a triangular prism = (1/2) x base x height x depth
2. Volume of a rectangular pyramid = base x height x depth
Given that the height of both shapes is 9 cm, we only need to determine the base and depth for each shape.
For the triangular prism, the base is a triangle with an area of 12 cm², and the depth is 6 cm. Therefore, the volume of the triangular prism is:
Volume = (1/2) x 12 cm² x 9 cm x 6 cm
Volume = 324 cm³
For the rectangular pyramid, the base is a rectangle with an area of 12 cm², and the depth is 6 cm. Therefore, the volume of the rectangular pyramid is:
Volume = 12 cm² x 9 cm x 6 cm
Volume = 648 cm³
Therefore, the volume of the triangular prism is 324 cm³, and the volume of the rectangular pyramid is 648 cm³.
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