Question

question 13 (multiple choice worth 1 point)
(06.01 mc)
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 6 units. which conclusion can be made from the given information?
o the volume of the triangular prism is half the volume of the cylinder.
o the volume of the triangular prism is twice the volume of the cylinder.
o the volume of the triangular prism is equal to the volume of the cylinder.
o the volume of the triangular prism is not equal to the volume of the cylinder.

Explanation:

Step1: Recall volume formulas

Volume of a prism \(V_{prism}=B\times h\) (where \(B\) is the base - area and \(h\) is the height), and volume of a cylinder \(V_{cylinder}=B\times h\) (where \(B\) is the base - area and \(h\) is the height). Given that the cross - sectional areas (base areas \(B\)) of the right - triangular prism and the right - cylinder are congruent (\(B_{prism}=B_{cylinder}\)) and their heights are equal (\(h_{prism}=h_{cylinder} = 6\)).

Step2: Calculate volumes

Substitute into the formulas: \(V_{prism}=B_{prism}\times h_{prism}\) and \(V_{cylinder}=B_{cylinder}\times h_{cylinder}\). Since \(B_{prism}=B_{cylinder}\) and \(h_{prism}=h_{cylinder}\), we have \(V_{prism}=V_{cylinder}\).

Answer:

The volume of the triangular prism is equal to the volume of the cylinder.