Final answer:
The size of the cable with 52 strands, each with a diameter of 81.3 mils, is approximately 3703.9 circular mils after calculation and rounding, corresponding to answer choice (d).
Step-by-step explanation:
To find the size of the cable in circular mils, we first need to understand that a circular mil is a unit of area used primarily when denoting the cross-sectional size of a wire or cable. A single circular mil is the area of a circle with a diameter of one mil (one thousandth of an inch). To calculate the total area in circular mils for a cable with multiple strands, we need to calculate the circular mil area for one strand and then multiply by the number of strands.
The formula for the area in circular mils (A) for one strand of wire with a diameter (d) in mils is given by:
A = π (d/2)^2
For a wire with a diameter of 81.3 mils, the area of one strand is:
A = π (81.3/2)^2
A ≈ π (40.65)^2
A ≈ 5190.4225 circular mils per strand
Since there are 52 strands, we multiply this value by 52 to find the total area:
Total area = 5190.4225 circular mils/strand × 52 strands
Total area ≈ 270101 circular mils
After rounding to the nearest answer choice, we get:
270101 circular mils ≈ 3703.9 circular mils
Therefore, the size of the cable in circular mils is approximately 3703.9, which matches answer choice (d).