Question

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.

Answer 1

The cross-sectional area of a wire with a diameter of 0.245 inches is 60,025 circular mils, calculated by converting inches to mils and then squaring the diameter.

Step-by-step explanation:

The cross-sectional area of a wire measures its ability to carry electrical current. In the electrical trades, the circular mil is a unit used for this purpose. The formula to find the cross-sectional area in circular mils given the diameter of the wire in inches is A = d², where d is the diameter of the wire in thousandths of an inch. To find the cross-sectional area of a wire with a diameter of 0.245 inches, we must convert this measurement into thousandths of an inch by multiplying by 1000, thus d = 245 mils. Then, we square this value to get the area: A = 245² = 60,025 circular mils.

Answer 2

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

STEP 1: Write the given sides

`diameter=0.245in`

STEP 2: Write the given formula for cross sectional area

`\begin{gathered} A=d^2 \\ where\text{ d is the diameter} \end{gathered}`

STEP 3: Find the cross sectional area

`\begin{gathered} A=d^2 \\ Area=0.245^2=0.060025in^2 \end{gathered}`

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.

`\begin{gathered} 1\text{ circular mil}=0.001^2=0.000001in^2 \\ x\text{ circular mil}=0.060025 \\ By\text{ cross multiplication,} \\ x=(0.060025)/(0.000001)=60,025circular\text{ }mils \end{gathered}`

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