Question

A cylinder rod formed from silicon is `46.0` `cm` long and has a mass of `3.00` `kg`. The density of silicon is `2.33` `g``/cm^3`. What is the diameter of the cylinder?

Answer 1

I make it 6 cm diameter (well....5.97 cm really, but it depends how many places you take `pi` to!).

Explanation:

You have been given density (d) and mass (m), so first you can determine volume (v).

`d = m/v` therefore `v = m/d` = `3000/2.33` = 1287.55 `cm^3`

Now you have the volume and the length (L) from which you can work out the cross sectional area, `pi.r^2`, and from that the diameter.
Volume v =`pi.r^2.L` therefore r = `sqrt(v/(pi.L))` and diameter D = 2r = `sqrt(v/(pi.L))`x 2.

So plugging in the numbers gives: D = `sqrt{1287.55/(3.142 X 46)` X2 = 5.97 cm.