Question
if a pyramid and prism both have this triangular base if both shapes have the same height and volume of the pyramid is 210cubic inches what is the volume of the prism
Answers
Answered by
GPT-4o mini
The volume of a pyramid is calculated using the formula:
\[
V_{\text{pyramid}} = \frac{1}{3} \cdot B \cdot h
\]
where \(B\) is the area of the base, and \(h\) is the height. For a prism, the volume is given by:
\[
V_{\text{prism}} = B \cdot h
\]
Given that both the pyramid and the prism have the same triangular base and the same height, we can relate their volumes.
Since you provided that the volume of the pyramid is 210 cubic inches, we can express the volume of the prism in terms of the volume of the pyramid:
\[
V_{\text{prism}} = 3 \cdot V_{\text{pyramid}}
\]
This is because the volume of a prism is three times that of a pyramid with the same base area and height.
So, substituting the volume of the pyramid:
\[
V_{\text{prism}} = 3 \cdot 210 = 630 \text{ cubic inches}
\]
Thus, the volume of the prism is **630 cubic inches**.
\[
V_{\text{pyramid}} = \frac{1}{3} \cdot B \cdot h
\]
where \(B\) is the area of the base, and \(h\) is the height. For a prism, the volume is given by:
\[
V_{\text{prism}} = B \cdot h
\]
Given that both the pyramid and the prism have the same triangular base and the same height, we can relate their volumes.
Since you provided that the volume of the pyramid is 210 cubic inches, we can express the volume of the prism in terms of the volume of the pyramid:
\[
V_{\text{prism}} = 3 \cdot V_{\text{pyramid}}
\]
This is because the volume of a prism is three times that of a pyramid with the same base area and height.
So, substituting the volume of the pyramid:
\[
V_{\text{prism}} = 3 \cdot 210 = 630 \text{ cubic inches}
\]
Thus, the volume of the prism is **630 cubic inches**.
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