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The normal (unsharpened) pencil is a hexagonal cylinder.
It is a cylinder when not sharpen
The volume is the length of the pencil multiplied by the cross sectional area. Cross Sectional Area = pi * radius2 in this case the radius is half the diameter, which is 0.15cm So, Cross Sectional Area = pi * (0.15 * 0.15) = 0.0707 cm2 So the total volume is 7cm * 0.0707 cm2 which is 0.4948 cm3
The number of the pencil is based on the type of carbon lead used inside. The thicker the carbon lead gets the higher the number of the pencil becomes. If you notice a mechanical pencil is 0.9mm in diameter so it would be called a #0.9 pencil. A #2 pencil's lead is 2mm in diameter. So Why would we call a pencil a #3 pencil? Because it's lead is 3mm in diameter.
An ordinary pencil is one example.