## To find : weight of steel per metre.

Since the formula to be derived is d^2/162, assumed cross section is circular and the material is cylinder.

Weight density of steel = 7850 kg/m^3.

### Formula:

Weight density = weight/volume.

Weight = weight density x volume.

Volume of cylinder= πh d^2 /4

h is the height of cylinder bar. = 1m

d is diameter in mm

Volume = 3.14/4 x d^2 x 10^-6.(converted mm to m two times for d)

Volume of cylindrical bar = (7.85 x 10^-7) d^2 cum

Weight of cylindrical bar

= 7850 x 7.85 x 10^-7 x d^2.

= 0.00616 x d^2

= d^2 /(0.00616^-1)

= d^2/162.3

~ d^2/162

Since d’s unit is converted into the formula from mm to m, you can directly use the dia number to find out the weight per metre. For example:

25 mm dia bar:

625/162 = 3.85 kg