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
Algebra ->
Customizable Word Problem Solvers
-> Geometry
-> 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
Log On
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?
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(½bh) = (6)½(1/4")(1/4")√3/2 = 3√3/32 in²
Then V = (3√3/32 in²)(8 in) = 3√3/4 in³ ≈ 1.3 in³
