Explanation:
To find the compressed volume of the cylinder, you can use the compression ratio. The compression ratio is defined as the ratio of the total cylinder volume (including both the compressed volume and the expanded volume) to the compressed volume alone.
Compression Ratio = Total Volume / Compressed Volume
Given that the compression ratio is 8.5 to 1 and the expanded volume is 51 cu in., you can set up the equation as follows:
8.5 = (Total Volume) / (Compressed Volume)
Now, we can solve for the compressed volume (V_compressed):
V_compressed = (Total Volume) / 8.5
To calculate the total volume, you can add the compressed volume (V_compressed) and the expanded volume (51 cu in.) together:
Total Volume = V_compressed + 51 cu in.
Now, substitute this into the equation:
V_compressed = (V_compressed + 51 cu in.) / 8.5
To isolate V_compressed, you can multiply both sides of the equation by 8.5:
8.5 * V_compressed = V_compressed + 51 cu in.
Now, subtract V_compressed from both sides:
7.5 * V_compressed = 51 cu in.
Now, divide both sides by 7.5 to solve for V_compressed:
V_compressed = (51 cu in.) / 7.5
V_compressed = 6.8 cu in.
So, the compressed volume of the cylinder is 6.8 cubic inches.