Question

4 cm

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?

prism: 216 cm ^3; pyramid:73 cm ^3
prism: 73 cm ^3; pyramid: 216 cm ^3
prism: 108 cm ^3; pyramid: 36 cm ^3
prism: 36 cm ^3; pyramid: 108 cm ^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the volume of the triangular prism, we need to find the area of the base triangle and then multiply it by the height of the prism.

Area of the base triangle = 1/2 * base * height
Area of the base triangle = 1/2 * 4 * 6
Area of the base triangle = 1/2 * 24
Area of the base triangle = 12 cm^2

Volume of the prism = Area of the base triangle * height
Volume of the prism = 12 * 9
Volume of the prism = 108 cm^3

To calculate the volume of the triangular pyramid, we need to find the volume of a pyramid formula which is given by:

Volume of pyramid = 1/3 * Area of the base triangle * height

Volume of pyramid = 1/3 * 12 * 9
Volume of pyramid = 1/3 * 108
Volume of pyramid = 36 cm^3

Therefore, the correct answer is:
prism: 108 cm^3; pyramid: 36 cm^3