Question

a square prism and a cylinder have the same height. the area of the cross - section of the square prism is 314 square units, and the area of the cross - section of the cylinder is 50π square units. based on this information, which argument can be made? the volume of the square prism is twice 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 half the volume of the cylinder. the volume of the square prism is ⅓ the volume of the cylinder.

Explanation:

Step1: Recall volume formulas

The volume formula for a prism is $V_{prism}=A_{base - prism}h$ and for a cylinder is $V_{cylinder}=A_{base - cylinder}h$. Given $A_{base - prism}=314$ square units, $A_{base - cylinder}=50\pi$ square units and they have the same height $h$.

Step2: Calculate volumes

$V_{prism}=314h$ and $V_{cylinder}=50\pi h$. Since $\pi\approx3.14$, then $V_{cylinder}=50\times3.14h = 157h$.

Step3: Compare volumes

We can see that $V_{prism}=2V_{cylinder}$ because $314h = 2\times157h$.

Answer:

The volume of the square prism is twice the volume of the cylinder.