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?
the 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.

Explanation:

Step1: Recall volume formulas

Volume of prism \(V_p=A\times h_p\) (where \(A\) is cross - sectional area and \(h_p\) is height of prism), volume of cylinder \(V_c = A\times h_c\) (where \(A\) is cross - sectional area and \(h_c\) is height of cylinder). Given \(h_p = 10\) and \(h_c=7\).

Step2: Calculate ratio of volumes

\(V_p=A\times10\) and \(V_c=A\times7\). Then \(\frac{V_p}{V_c}=\frac{A\times10}{A\times7}=\frac{10}{7}\approx1.43\). So \(V_p
eq V_c\)

Answer:

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