SOLUTION: A lead pencil whose ends are regular hexagons was cut from a cylindrical piece of wood with the least waste.If the original piece was 8 in.long and 1\4in.in diameter.Find the volum

Question 985186: A lead pencil whose ends are regular hexagons was cut from a cylindrical piece of wood with the least waste.If the original piece was 8 in.long and 1\4in.in diameter.Find the volume of the pencil?

Answer by srinivas.g(540) (Show Source): You can put this solution on YOUR website!
A hexagon may be viewed as 6 equilateral triangles with a common apex. Given "the least waste", the side of each of these triangles is s = 1/4 in.
So the base of 1 triangle is b = 1/4 in; the height for an equilateral triangle can be shown to be h = b√3/2, so the total area of the pencil is
A = 6(�bh) = (6)�(1/4")(1/4")√3/2 = 3√3/32 in�
Then V = (3√3/32 in�)(8 in) = 3√3/4 in� ≈ 1.3 in�
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