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: 108 cm3; pyramid: 36 cm3
prism: 108 cm cubed ; pyramid: 36 cm cubed
prism: 216 cm3; pyramid: 72 cm3
prism: 216 cm cubed ; pyramid: 72 cm cubed
prism: 36 cm3; pyramid: 108 cm3
prism: 36 cm cubed ; pyramid: 108 cm cubed
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prism: 72 cm3; pyramid: 216 cm3
The volume of a triangular prism is calculated by multiplying the base area (1/2 * base * height) by the height. In this case, the base area is 1/2 * 6 * 4 = 12 square cm. This multiplied by the height of the prism (9 cm) gives a volume of 72 cubic cm.
The volume of a triangular pyramid is calculated by multiplying the base area by the height and dividing by 3. The base area is the same as the prism, 12 square cm, multiplied by the height and divided by 3 gives a volume of 216 cubic cm.