Question

What is the cross-sectional area of a wire if its outside diameter is 0.0625 inch?

Answer 1

Answer: 0.0031 in²

Step-by-step explanation:

Formula: CSA = CSA = πD² / 4 = 0.785 x D²

in which,

CSA = cross-sectional area of the wire, (in²)

D = outside diameter of the wire, (in)

π/4 = 0.785, a constant value

* (3.14 / 4 = 0.785) - this will always be a constant value.

There are two ways to find the CSA of a wire.

1. πD² / 4

3.14(0.0625²) / 4

First multiply or square the diameter which is 0.0625

0.0625 x 0.0625 = 0.00390625

Second multiply 3.14 which is pi times the squared diameter

3.14 x 0.00390625 = 0.012265625

Last divide by 4

0.012265625 / 4 = 0.0030664062 in²

Round off and you will get 0.0031 in²

2. 0.785 x D²

whereas, 0.785 is always a constant of π divided by 4

0.785 x 0.0625²

First multiply or square the diameter which is 0.0625

0.0625 x 0.0625 = 0.00390625

Last multiply the constant value of 0.785 by the value squared

0.785 x 0.00390625 = 0.0030664062 in²

Round off and you will get 0.0031 in²

* Hint - it is easier to remember that the constant value is 0.785

Answer 2

Given that the diameter: d= 0.0625 inch.

So, radius of the wire : r =
`(0.0625)/(2)` = 0.03125 inch

Now the formula to find the cross-sectional area of wire ( circle) is:

A = πr²

= 3.14 * (0.03125)² Since, π = 3.14 and r = 0.03125

=3.14 * 0.000976563

= 0.003066406

= 0.00307 (Rounded to 5 decimal places).

Hence, cross-sectional area of a wire is 0.00307 square inches.

Hope this helps you!