The volume of a prism is given by V = base area x height.
Since the base is an equilateral triangle, the area can be calculated using the formula A = (sqrt(3) / 4) x side^2.
Therefore, the base area of the prism is A = (sqrt(3) / 4) x 6^2 = 9sqrt(3) cm^2.
So, the volume of the prism is V = 9sqrt(3) cm^2 x 9 cm = 81sqrt(3) cm^3 ≈ 140.12 cm^3.
The volume of a pyramid is given by V = (1/3) x base area x height.
Therefore, the volume of the pyramid is V = (1/3) x 9sqrt(3) cm^2 x 9 cm = 27sqrt(3) cm^3 ≈ 46.74 cm^3.
Therefore, the correct response is: prism: 140.12 cm^3; pyramid: 46.74 cm^3.
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: 216 cm3; pyramid: 72 cm3
prism: 108 cm3; pyramid: 36 cm3
prism: 36 cm3 ; pyramid: 108 cm3
prism: 72 cm3; pyramid: 216 cm3
1 answer