Question

question 2 multiple choice (worth 1 point) (08.01b mc) the cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 2 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder.

Explanation:

Step1: Define volume formulas

Volume of a prism (or cylinder) is $V = A_{base} \times h$, where $A_{base}$ is cross-sectional area, $h$ is height.

Step2: Assign given values

Let $A$ = congruent cross-sectional area.
For triangular prism: $V_{prism} = A \times 2$
For cylinder: $V_{cylinder} = A \times 6$

Step3: Compare the volumes

$\frac{V_{prism}}{V_{cylinder}} = \frac{2A}{6A} = \frac{1}{3}$, so volumes are not equal.

Answer:

The volume of the triangular prism is not equal to the volume of the cylinder