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The circular mil is a unit used in electrical trades to indicate the cross-sectional area of wires. The cross-sectional area of a wire in circular mils is given by the formula A=d², where d is the diameter of the wire in thousandths of an inch. Find the cross-sectional area of a wire in circular mils if the diameter is 0.245 in.The cross-sectional area of the wire is ___ circular mils.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given sides

[tex]diameter=0.245in[/tex]

STEP 2: Write the given formula for cross sectional area

[tex]\begin{gathered} A=d^2 \\ where\text{ d is the diameter} \end{gathered}[/tex]

STEP 3: Find the cross sectional area

[tex]\begin{gathered} A=d^2 \\ Area=0.245^2=0.060025in^2 \end{gathered}[/tex]

STEP 4: Convert to circular mils

A circular mil is the equivalent area of a circle whose diameter is 0.001 (10-3) inch, or approximately 0.7854 millionths of a square inch.

[tex]\begin{gathered} 1\text{ circular mil}=0.001^2=0.000001in^2 \\ x\text{ circular mil}=0.060025 \\ By\text{ cross multiplication,} \\ x=\frac{0.060025}{0.000001}=60,025circular\text{ }mils \end{gathered}[/tex]

Hence, the cross sectional area of the wire is 60025 circular mils

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