# 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?

Sep 12, 2016

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).

$d = \frac{m}{v}$ therefore $v = \frac{m}{d}$ = $\frac{3000}{2.33}$ = 1287.55 $c {m}^{3}$

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 = $\sqrt{\frac{v}{\pi . L}}$ and diameter D = 2r = $\sqrt{\frac{v}{\pi . L}}$x 2.

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