SOLUTION: 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

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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.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2Ar%5E2%2Ah
and
the vol of a cone is: %281%2F3%29%2Api%2Ar%5E2%2Ah
therefore
the vol of the shavings: %282%2F3%29%2Api%2Ar%5E2%2Ah
v = %282%2F3%29%2Api%2A.5%5E2%2A2
v = %282%2F3%29%2Api%2A.25%2A2
v = %282%2F3%29%2A1.5708
v = 1.047 cu/cm