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

1,092 cubic units
1,092 cubic units

364 cubic units
364 cubic units

728 cubic units
728 cubic units

3,276 cubic units
3,276 cubic units
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1 answer

The volume \( V \) of a prism is calculated using the formula:

\[ V = B \times h \]

where \( B \) is the area of the base and \( h \) is the height. For a pyramid with the same base and height as the prism, the volume \( V_p \) is given by:

\[ V_p = \frac{1}{3} B \times h \]

From the information given, the volume of the prism is 1,092 cubic units:

\[ 1,092 = B \times h \]

Now, substituting this into the formula for the volume of the pyramid gives:

\[ V_p = \frac{1}{3} (B \times h) = \frac{1}{3} (1,092) = 364 \]

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

The correct response is:

364 cubic units