http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w13_qp_53.pdf
q7)

Question

http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w13_qp_53.pdf
q7)

abmon98 · Answer

The uniform solid consists of both a cone and a cylinder, now the centre of mass of the cone is 3/4 from the vertex. The cylinder is geometrically symmetric so its centre of mass lies at 0.2 m away from the origin point. How can i calculate their masses.

theeric · Answer

You actually can't calculate their masses without knowing their densities! For this problem, it seems that you have to assume that the densities are constant throughout each shape and the same as each other. But you are just told what the mass is.

theeric · Answer

I think that you $\it{can }$ find the mass as a multiple of $\rho$ (or whatever variable you use for density)

abmon98 · Answer

its of uniform thickness, so mass is proportional to their areas.

theeric · Answer

Well, volumes, right?

abmon98 · Answer

why?

theeric · Answer

Well, they're cylinders and cones, so we're definitely looking at volumes. And maybe we can consider the cross-sectional areas - I'm not sure! I'd have to do the math both ways.

theeric · Answer

Just thinking about it, the area should suffice! But we need to consider the volume because it is proportional to the mass - so the volume is handy to find the center of mass.

theeric · Answer

You could just use the volume formulas, find the ratio between them, and then you'll know how much each volume's center of mass "counts."

What ways were you taught to solve a problem like this?

irishboy123 · Answer

this is a "solid" shape.  if you do the math assuming, as @theEric suggests, a constant density, all will be fine provided you go by volume.

going by area is just nuts.

theeric · Answer

Haha, @IrishBoy123 , nuts, but it does give some information.

@Abmon98 , do you use integration?

theeric · Answer

And I think the more general method for volumes would be to consider the solid shapes, as @IrishBoy123 mentioned.

abmon98 · Answer

no i do not use integration, thanks for your help.

irishboy123 · Answer

you do not need integration to do this.  you just need the formula for the volumes of the shapes.  i can show you if you are still interested.