Question

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 argument can be made? the volume of the square prism is 1/3 the volume of the cylinder. the volume of the square prism is half the volume of the cylinder. the volume of the square prism is equal to the volume of the cylinder. the volume of the square prism is twice the volume of the cylinder.

Explanation:

Step1: Recall volume formulas

The volume of a prism \(V_{prism}=A_{base}\times h\) and the volume of a cylinder \(V_{cylinder}=A_{circular - base}\times h\), where \(h\) is the height and \(A\) is the cross - sectional area. Let the height of both the square prism and the cylinder be \(h\), the cross - sectional area of the square prism \(A_{1} = 628\) square units and the cross - sectional area of the cylinder \(A_{2}=200\pi\) square units.

Step2: Calculate volumes

The volume of the square prism \(V_{1}=A_{1}h = 628h\). The volume of the cylinder \(V_{2}=A_{2}h=200\pi h\approx200\times3.14h = 628h\).

Step3: Compare volumes

Since \(V_{1}=628h\) and \(V_{2}=628h\), the volume of the square prism is equal to the volume of the cylinder.

Answer:

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