Question
Question
Use the image to answer the question.
An illustration shows a triangle with sides measuring 21, 17, and 10. A perpendicular line, from the side measuring 21 to the opposite angle, measures 8. A right angle symbol is shown to the left of the perpendicular line.
A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 1,092 cubic units, what is the volume of the pyramid?
(1 point)
Responses
3,276 cubic units
3,276 cubic units
364 cubic units
364 cubic units
728 cubic units
728 cubic units
1,092 cubic units
1,092 cubic units
Skip to navigation
Use the image to answer the question.
An illustration shows a triangle with sides measuring 21, 17, and 10. A perpendicular line, from the side measuring 21 to the opposite angle, measures 8. A right angle symbol is shown to the left of the perpendicular line.
A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 1,092 cubic units, what is the volume of the pyramid?
(1 point)
Responses
3,276 cubic units
3,276 cubic units
364 cubic units
364 cubic units
728 cubic units
728 cubic units
1,092 cubic units
1,092 cubic units
Skip to navigation
Answers
Answered by
GPT-4o mini
To find the volume of the pyramid, we first need to understand the relationship between the volumes of the prism and the pyramid, both of which use the same triangular base.
The volume \( V \) of a prism can be calculated using the formula:
\[
V_{\text{prism}} = \text{Base Area} \times \text{Height}
\]
The volume \( V \) of a pyramid is given by the formula:
\[
V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
From the problem, we know that the volume of the prism is 1,092 cubic units:
\[
V_{\text{prism}} = 1,092 \, \text{cubic units}
\]
Since both shapes have the same height and base area, the volume of the pyramid is one-third that of the prism:
\[
V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}} = \frac{1}{3} \times 1,092 = 364 \, \text{cubic units}
\]
Thus, the volume of the pyramid is **364 cubic units**.
The volume \( V \) of a prism can be calculated using the formula:
\[
V_{\text{prism}} = \text{Base Area} \times \text{Height}
\]
The volume \( V \) of a pyramid is given by the formula:
\[
V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
From the problem, we know that the volume of the prism is 1,092 cubic units:
\[
V_{\text{prism}} = 1,092 \, \text{cubic units}
\]
Since both shapes have the same height and base area, the volume of the pyramid is one-third that of the prism:
\[
V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}} = \frac{1}{3} \times 1,092 = 364 \, \text{cubic units}
\]
Thus, the volume of the pyramid is **364 cubic units**.