The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 10 units, and the right cylinder has a height of 7 units. Which conclusion can be made from the given information?Group of answer choicesThe volume of the prism is half the volume of the cylinder.The volume of the prism is not equal to the volume of the cylinder.The volume of the prism is twice the volume of the cylinder.The volume of the prism is equal to the volume of the cylinder.
Question
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 10 units, and the right cylinder has a height of 7 units. Which conclusion can be made from the given information?Group of answer choicesThe volume of the prism is half the volume of the cylinder.The volume of the prism is not equal to the volume of the cylinder.The volume of the prism is twice the volume of the cylinder.The volume of the prism is equal to the volume of the cylinder.
Solution
The volume of a 3D shape is calculated by multiplying the cross-sectional area by the height. In this case, both the triangular prism and the right cylinder have the same cross-sectional area, but different heights.
The volume of the triangular prism would be the cross-sectional area times the height of 10 units. The volume of the right cylinder would be the cross-sectional area times the height of 7 units.
Since the cross-sectional areas are the same, the volume of the triangular prism is greater than the volume of the right cylinder because 10 units is greater than 7 units.
Therefore, the correct conclusion from the given information is: The volume of the prism is not equal to the volume of the cylinder.
Similar Questions
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.
Find the volume of the triangular prism.
e horizontal cross-sectional shapes of the given prism are all congruent.A.TrueB.False
The prism below has a cross‑sectional area of 27 cm227cm 2 and a length of 3 cm3cm.Calculate the volume of the prism.Give your answer in cm3cm 3 .
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