The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 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 twice the volume of the cylinder.The volume of the prism is equal to the volume of the cylinder.The volume of the prism is not 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 5 units, and the right cylinder has a height of 5 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 twice the volume of the cylinder.The volume of the prism is equal to the volume of the cylinder.The volume of the prism is not equal to the volume of the cylinder.
Solution
The volume of the prism is equal to the volume of the cylinder.
Here's why:
The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.
In this case, we're told that the cross-sectional areas (which are the same as the base areas for these shapes) of the prism and the cylinder are congruent, or equal. We're also told that the heights of the two shapes are equal.
Therefore, since the base areas and the heights are the same for both shapes, their volumes will also be the same.
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
Find the volume of this triangular prism.Be sure to include the correct unit in your answer.5cm7cm8cm
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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