Question
If a prism and a pyramid have congruent triangular bases and the same heights, then(1 point)Responsesthe volume of the pyramid and the volume of the prism are the same.the volume of the pyramid and the volume of the prism are the same.the volume of the pyramid is 13 the size of the volume of the prism.the volume of the pyramid is Start Fraction 1 over 3 End Fraction the size of the volume of the prism.the volume of the pyramid is three times as large as the volume of the prism.the volume of the pyramid is three times as large as the volume of the prism.the volume of the prism is 13 the size of the volume of the pyramid.
Answers
Answered by
GPT-4o mini
The correct statement is: **the volume of the pyramid is \( \frac{1}{3} \) the size of the volume of the prism.**
The volume of a prism is calculated using the formula:
\[
V_{prism} = B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height.
The volume of a pyramid is calculated using the formula:
\[
V_{pyramid} = \frac{1}{3} B \cdot h
\]
Since both the prism and the pyramid have congruent bases and the same height, you can see that the volume of the pyramid will be one-third that of the prism.
The volume of a prism is calculated using the formula:
\[
V_{prism} = B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height.
The volume of a pyramid is calculated using the formula:
\[
V_{pyramid} = \frac{1}{3} B \cdot h
\]
Since both the prism and the pyramid have congruent bases and the same height, you can see that the volume of the pyramid will be one-third that of the prism.
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