Problema Solution
A lead pencil whose ends are regular hexagon was cut from a cylindrical piece of wood, with the least waste. If the original piece was 8 inches .long and ½ inches in diameter, find the volume of a pencil?
Answer provided by our tutors
Area of the base= Area of hexagon = (3√3/2 )*(D/2)^2
=(3√3/2 )*((1/2)/2)^2 = (3√3/32 ) sq.inch
Volume of Pencil = Area of base * Height
= (3√3/32 )*8 =(3√3/4 )
Volume of pencil = (3√3/4) = 1.3 cubic inches