How Do You Calculate the Mass of a Steel I-Beam?

[mynameiscool]

Homework Statement

a structural I-beam is made of steel. a view of its cross section and its dimensions are shown in the figure below. as seen in the figure, L=13.2cm, H=37.4cm, W=1.41cm. what is the mass of a section 1.25m long? the density of steel is 7.56x10^3kg/m^3

i attached a picture of the beam

Homework Equations

volume=LxHxW
m=dv

The Attempt at a Solution

1. i converted values to meters:
L=0.132m
H=0.374m
W=0.0141m

2.find the volume for the top and bottom rectangles ( they are both same measurements)
so... v=lxhxw
v=0.132mx0.0141mx1.25m
=2.3265x10^-3 m^3

since top and bottom rectangles are same so add
2.3265x10^-3 m^3+2.3265x10^-3 m^3= 4.653x10^-3 m^3

then found volume for middle rectangle
but first found its height 37.4-0.0141-0.0141=37.3718
v=lxwxh
37.3718mx0.0141mx1.25m=0.65m^3

3. m=dv so..
first add volumes= 4.653x10^-3m^3+0.65m^3=0.654
then 0.654m^3x7.56x10^3kg/m^3
=4949kg
and my answer is wrong ! :( please help ASAP i can't figure it out
take a look at my long solution and help me :)

 

[haruspex]

volume=LxHxW

Yes, but only for a rectangular block, and the lengths L, H, W must be mutually perpendicular.

2.find the volume for the top and bottom rectangles

A rectangle has area, not volume. Just because the distances are called L, H and W doesn't mean that they plug naturally into a formula you know that has variables with those names. Variable names are just names; it's what they stand for that's important.
Find the area of the cross-section.

 

[mynameiscool]

Yes, but only for a rectangular block, and the lengths L, H, W must be mutually perpendicular.

A rectangle has area, not volume. Just because the distances are called L, H and W doesn't mean that they plug naturally into a formula you know that has variables with those names. Variable names are just names; it's what they stand for that's important.
Find the area of the cross-section.

area of the cross section as in Lxw ? i did that and i still got the wrong answer too
can you please explain step by step ?

 

[SteamKing]

In your calculation of the middle rectangle, you have used H = 37.4 rather than H = 0.374. This is why your calculation is incorrect.

BTW, you do not necessarily have to find the area of the cross section unless you are specifically asked for it. Multiplying the area of each individual rectangle by the length of the beam and adding the resulting volumes together will give the same answer as multiplying the area of the cross section by the length.