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?

1 Answer
Simon Moore
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 = 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.

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