Question
A prism and a pyramid both have this triangular case. If both shapes have the same height and the volume of the prism is 600 ft3 what is the volume of the pyramid?
Picture shows length of 20 feet,the height is 6ft going up to create a triangle to the left
1,800 ft3
600 ft 3
400 ft3
200ft 3
Picture shows length of 20 feet,the height is 6ft going up to create a triangle to the left
1,800 ft3
600 ft 3
400 ft3
200ft 3
Answers
Answered by
GPT-4o mini
To find the volume of the pyramid when we know the volume of the prism, we can use the relationship between the volumes of these two shapes.
The volume \( V \) of a prism is calculated as:
\[
V_{\text{prism}} = B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height.
The volume \( V \) of a pyramid is calculated as:
\[
V_{\text{pyramid}} = \frac{1}{3} B \cdot h
\]
This means that the volume of the pyramid is one-third of the volume of the prism if they have the same base area and height.
Given that the volume of the prism is 600 ft³, we can calculate the volume of the pyramid as follows:
\[
V_{\text{pyramid}} = \frac{1}{3} V_{\text{prism}} = \frac{1}{3} \cdot 600 \text{ ft}^3 = 200 \text{ ft}^3
\]
Thus, the volume of the pyramid is **200 ft³**.
The volume \( V \) of a prism is calculated as:
\[
V_{\text{prism}} = B \cdot h
\]
where \( B \) is the area of the base and \( h \) is the height.
The volume \( V \) of a pyramid is calculated as:
\[
V_{\text{pyramid}} = \frac{1}{3} B \cdot h
\]
This means that the volume of the pyramid is one-third of the volume of the prism if they have the same base area and height.
Given that the volume of the prism is 600 ft³, we can calculate the volume of the pyramid as follows:
\[
V_{\text{pyramid}} = \frac{1}{3} V_{\text{prism}} = \frac{1}{3} \cdot 600 \text{ ft}^3 = 200 \text{ ft}^3
\]
Thus, the volume of the pyramid is **200 ft³**.
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