In the figure below, the dimensions of an unsharpened pencil are given. The unsharpened pencil have graphite in a cylindrical shape, surrounded by wood. The diameter of the graphite is 2mm. The density of graphite is $640\text{ kg/m}^3$. The density of wood is $420\text{ kg/m}^3$. Find the mass of 500 pencils.
My attempt was the following:
I found the volume of the wood: $$3.14\times (0.004)^2\times 0.15= 0.000007536$$
The volume of graphite:
$$3.14\times (0.001)^2\times 0.15= 0.000000471$$
I found the mass of 1 pencil: $$0.000007536\times 420 + 0.000000471\times 640= 0.0034\\
0.0034\times 500= 1.7 \text{ kg}$$
I think I messed up the solution!
All help/solutions appreciated.
Thanks
Best Answer
first of all, I'd like to say it would be much easier for you to calculate with, say, $4.71×10^7$ instead of $0.000000471$. The mistake you're making here is counting the graphite's volume twice. When calculating the volume of the wooden part, you need to subtract the graphite's volume:
$7.536×10^{-6}-0.471×10^{-7}=10^{-7}×(75.36-0.471)=74.889×10^{-7}=7.4889×10^{-6} m^3$
Now, you have the density of both materials. That is to say, you know how many $kg$ one $m^3$ of wood/graphite weighs. From that info, you can calculate the mass of wood/graphite in one pencil:
$m_{wood}=7.4889×10^{-8}×420=3145.338×10^{-8}=3.145338×10^{-5}kg$
$m_{graphite}=0.471×10^{-7}×640=301.44×10^{-7}=3.0144×10^{-5}kg$
$m_{pencil}=m_{wood}+m_{graphite}=10^{-5}×(3.0144+3.145338)=6.159738×10^{-5}kg$
Now getting the mass of 500 pencils is simple! The answer is
$6.159738×500×10^{-5}=30.79869×10^{-3}kg \approx 30.8 gr$
Hopefully this solves your problem :)