Question

the cross - sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 4 units. which conclusion can be made from the given information? the volume of the triangular prism is not equal to the volume of the cylinder. the volume of the triangular prism is 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 half the volume of the cylinder.

Explanation:

Step1: Recall volume formulas

Volume of cylinder \(V_{c}=A_{c}h_{c}\), volume of triangular - prism \(V_{t}=A_{t}h_{t}\), where \(A\) is cross - sectional area and \(h\) is height. Given \(A_{c}=A_{t}\), \(h_{c} = 4\) and \(h_{t}=6\).

Step2: Calculate volumes

\(V_{c}=A\times4\) and \(V_{t}=A\times6\) (where \(A = A_{c}=A_{t}\)).

Step3: Compare volumes

\(\frac{V_{t}}{V_{c}}=\frac{A\times6}{A\times4}=\frac{3}{2}\), so \(V_{t}=\frac{3}{2}V_{c}\), or \(V_{c}=\frac{2}{3}V_{t}\), which means the volume of the triangular prism is not equal to the volume of the cylinder.

Answer:

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