Use the image to answer the question.

An illustration shows an equilateral triangle with each side measuring 6 centimeters. The perpendicular height is shown as a dashed line from the base to the apex and and is 4 centimeters. A right angle symbol is shown to the right of the perpendicular line.

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)
Responses

prism: 72 cm3; pyramid: 216 cm3
prism: 72 cm cubed ; pyramid: 216 cm cubed

prism: 216 cm3; pyramid: 72 cm3
prism: 216 cm cubed ; pyramid: 72 cm cubed

prism: 108 cm3; pyramid: 36 cm3
prism: 108 cm cubed ; pyramid: 36 cm cubed

prism: 36 cm3; pyramid: 108 cm3
prism: 36 cm cubed ; pyramid: 108 cm cubed

1 answer

prism: 108 cm3; pyramid: 36 cm3
prism: 108 cm cubed ; pyramid: 36 cm cubed

To find the volume of a triangular prism, you multiply the area of the base (area of the equilateral triangle = 1/4 * sqrt(3) * s^2, where s is the side length) by the height of the prism.
Prism volume = (1/4 * sqrt(3) * 6^2) * 9 = 108 cm3

To find the volume of a triangular pyramid, you multiply the area of the base (area of the equilateral triangle) by the height of the pyramid and divide by 3.
Pyramid volume = ((1/4 * sqrt(3) * 6^2) * 9) / 3 = 36 cm3

Therefore, the correct answer is prism: 108 cm3; pyramid: 36 cm3.