Question 243267
A cylindrical end of a pencil is sharpened to produce a perfect cone at the end with no overall loss of length.
 If the diameter of the pencil is 1cm, and the cone is of length 2cm, calculate the volume of the shavings.
:
radius of the pencil = .5cm
:
the vol of cylinder is {{{pi*r^2*h}}}
 and
the vol of a cone is: {{{(1/3)*pi*r^2*h}}} 
therefore
the vol of the shavings: {{{(2/3)*pi*r^2*h}}}
v = {{{(2/3)*pi*.5^2*2}}}
v = {{{(2/3)*pi*.25*2}}}
v = {{{(2/3)*1.5708}}} 
v = 1.047 cu/cm