A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 628 square units, and the area of the cross-section of the cylinder is 200π square units. Based on this information, which argument can be made?Group of answer choicesThe volume of the square prism is the volume of the cylinder.The volume of the square prism is half the volume of the cylinder.The volume of the square prism is equal to the volume of the cylinder.The volume of the square prism is twice the volume of the cylinder.
Question
A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 628 square units, and the area of the cross-section of the cylinder is 200π square units. Based on this information, which argument can be made?Group of answer choicesThe volume of the square prism is the volume of the cylinder.The volume of the square prism is half the volume of the cylinder.The volume of the square prism is equal to the volume of the cylinder.The volume of the square prism is twice the volume of the cylinder.
Solution
The volume of a prism or a cylinder is given by the formula: Volume = Area of cross-section * Height.
Given that the height is the same for both the square prism and the cylinder, we can compare their volumes by comparing the areas of their cross-sections.
The area of the cross-section of the square prism is 628 square units, and the area of the cross-section of the cylinder is 200π square units.
To compare these two areas, we need to convert the area of the cylinder to the same units as the square prism. We know that π is approximately 3.14, so 200π is approximately 628.
Therefore, the area of the cross-section of the square prism is equal to the area of the cross-section of the cylinder.
Since the volumes of the prism and the cylinder are proportional to the areas of their cross-sections, we can conclude that the volume of the square prism is equal to the volume of the cylinder.
Similar Questions
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