Question

question 5 multiple choice worth 4 points) (08.01 mc) 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 statement can be made? o the volume of the square prism is 1/3 the volume of the cylinder. o the volume of the square prism is half the volume of the cylinder. o the volume of the square prism is equal to the volume of the cylinder. o the volume of the square prism is twice the volume of the cylinder.

Explanation:

Step1: Recall volume formulas

Volume of prism \(V_{prism}=A_{prism - cross - section}\times h\), volume of cylinder \(V_{cylinder}=A_{cylinder - cross - section}\times h\).

Step2: Substitute given areas

Given \(A_{prism - cross - section}=628\), \(A_{cylinder - cross - section}=200\pi\approx 200\times3.14 = 628\).
Since \(V_{prism}=A_{prism - cross - section}\times h\) and \(V_{cylinder}=A_{cylinder - cross - section}\times h\) and \(A_{prism - cross - section}=A_{cylinder - cross - section}\) (both equal to \(628\)) and \(h\) (height) is the same for both.

Answer:

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