Question

For a wire with a circular cross section and a diameter = 3.00mm calculate the following: (m means meter. mm means millimeter. cm means centimeter.) Calculate the cross sectional area in mm2. Calculate the cross sectional area in cm2

Answer 1

The cross sectional area in mm2 is 7.07
`mm^(2)`

The cross sectional area in cm2 is 0.0707
`cm^(2)`

Step-by-step explanation:

The cross-sectional area (a) of the wire is given by;

a =
`\pi` x
`(d^(2) )/(4)`

where d is the diameter of the cross section = 3.00mm

1 => To find the cross-sectional area in
`mm^(2)`, substitute the value of d = 3.00mm into the equation above as follows;

a =
`\pi` x
`(3.00^(2) )/(4)`

Taking
`\pi` to be
`(22)/(7)` we have;

a =
`(22)/(7)` x
`(3.00^(2) )/(4)`

a = 7.07
`mm^(2)`

2 => To find the cross-sectional area in
`cm^(2)`, first convert the diameter in mm to cm as follows;

3.00mm = 0.3cm

Now, substitute the value of d = 0.3cm into the equation above as follows;

a =
`\pi` x
`(0.3^(2) )/(4)`

Taking
`\pi` to be
`(22)/(7)` we have;

a =
`(22)/(7)` x
`(0.3^(2) )/(4)`

a = 0.0707
`cm^(2)`