Physics help! What is the mass....?

Question

A structural I steal beam has a density of 7.56 x 10^3 kg/m^3.

What is the mass of a section 1.50 m long?

And it shows a figure of an I beam, the top is 15 cm long, the side is 36 cm long, the widths of the 3 parts of the I are 1.cm wide.

so m=pV, I know the density, but how do I figure out the volume?

Somethin to do with Area times height, but I'm not gettin it right....

I got .54m^3 as the volume and that's wrong.....

Answer 1

Look it up.

Answer 2

You're right: mass = density x volume

You know the density.

Volume = area x length
You know the length. You need the area of the cross-section of the I-beam.

In structural engineering, there are standard tables that tell you the area of an I-beam depending on the shape of it. However, from the dimensions you've been given, it looks like it's a simply I-beam. It therefore has three parts: the long vertical middle section and the shorter horizontal end pieces. Break this up into three rectangles and add them for the area.

Area = (long section) + (2 x end section)
= (36cm x 1cm) + (2 x 15cm x 1 cm)
= 36cm^2 + 30cm^2
= 66 cm^2
= 66 x 10^-4 m^2

So, the volume = area x length
= 66 x 10_4 m^2 x 1.5m
= 9.9 x 10^-5 m^3

So the mass = density x volume
= 7.56x10^3 kg/m^3 x 9.9x10^-5 m^3
= 0.75 kg

That seems light: I may have made a math error in there, but that's the procedure.