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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

728 cubic units
728 cubic units

364 cubic units
364 cubic units

1,092 cubic units
1,092 cubic units

3,276 cubic units
3,276 cubic units
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Answer 1

To find the volume of the pyramid given that both the prism and the pyramid share the same triangular base and height, we need to remember the formula for the volume of both shapes:

1. Volume of a prism: \[ V = \text{Base Area} \times \text{Height} \]

2. Volume of a pyramid: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Since the volume of the prism is given as 1,092 cubic units, we can denote the base area as \( A \) and the height as \( h \). Thus, we have: \[ 1,092 = A \times h \]

For the pyramid, the volume is: \[ V = \frac{1}{3} \times A \times h \]

Now substituting \( A \times h \) with 1,092 into the pyramid's volume formula: \[ V = \frac{1}{3} \times 1,092 \] \[ V = \frac{1,092}{3} = 364 \]

Thus, the volume of the pyramid is 364 cubic units.

The correct response is: 364 cubic units.