Shrunk Fabric Circumference Calculation

This solution determines the final circumference of a tubular knitted fabric after shrinkage, using the machine's specifications and the given shrinkage percentage.

Calculating Initial Circumference

The circumference of the fabric as it is knitted is based on the diameter of the needle bed.

• Needle Bed Diameter = 20 inches
• The formula for circumference is $C = \pi \times D$, where $D$ is the diameter.
• Initial Circumference ($C_{\text{initial}}$) = $\pi \times 20 \text{ inches}$
• $C_{\text{initial}} \approx 3.14159 \times 20 \approx 62.83 \text{ inches}$

Applying Course-wise Shrinkage

The fabric shrinks by 35% in the course-wise direction. The course direction corresponds to the circumference in a tubular fabric.

• Shrinkage Percentage = 35%
• Remaining Percentage = $100\% - 35\% = 65\%$
• The final circumference will be 65% of the initial circumference.

Determining Shrunk Circumference

Calculate the final circumference after shrinkage.

• Shrunk Circumference ($C_{\text{shrunk}}$) = $C_{\text{initial}} \times (\text{Remaining Percentage})$
• $C_{\text{shrunk}} = (\pi \times 20 \text{ inches}) \times 0.65$
• $C_{\text{shrunk}} \approx 62.83 \text{ inches} \times 0.65$
• $C_{\text{shrunk}} \approx 40.84 \text{ inches}$

This value is approximately 40.9 inches, matching Option A.