To find the compressed volume of a cylinder given the compression ratio and the expanded volume, follow these steps:
1. Identify the expanded volume: The expanded volume of the cylinder is given as 21 cubic inches.
2. Understand the compression ratio: The compression ratio is 10.5:1, which means the expanded volume of the cylinder is 10.5 times the compressed volume.
3. Set up the relationship: If [tex]\( V_{\text{expanded}} \)[/tex] is the expanded volume and [tex]\( V_{\text{compressed}} \)[/tex] is the compressed volume, the relationship can be written as:
[tex]\[
V_{\text{expanded}} = 10.5 \cdot V_{\text{compressed}}
\][/tex]
4. Substitute the known value: Substitute the given expanded volume (21 cubic inches) into the equation:
[tex]\[
21 = 10.5 \cdot V_{\text{compressed}}
\][/tex]
5. Solve for the compressed volume: To find [tex]\( V_{\text{compressed}} \)[/tex], divide both sides of the equation by 10.5:
[tex]\[
V_{\text{compressed}} = \frac{21}{10.5}
\][/tex]
6. Simplify the expression:
[tex]\[
V_{\text{compressed}} = 2
\][/tex]
Therefore, the compressed volume of the cylinder is [tex]\( 2 \)[/tex] cubic inches.
