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 $\frac{1}{3}$ 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 formula for a prism is $V_{prism}=A_{base}\times h$, and for a cylinder is $V_{cylinder}=A_{base}\times h$, where $A_{base}$ is the cross - sectional area and $h$ is the height.

Step2: Analyze given conditions

We are given that the height of the square prism and the cylinder is the same, and the cross - sectional area of the square prism ($A_{1}$) is equal to the cross - sectional area of the cylinder ($A_{2}$), i.e., $A_{1}=A_{2}$ and $h_{1}=h_{2}$.

Step3: Calculate volumes

$V_{prism}=A_{1}h_{1}$ and $V_{cylinder}=A_{2}h_{2}$. Since $A_{1} = A_{2}$ and $h_{1}=h_{2}$, we have $V_{prism}=V_{cylinder}$.

Answer:

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