6

Part of 2008 Stanford Mathematics Tournament

Problems(1)

Sharpening a Pencil

Source:

A round pencil has length

8

when unsharpened, and diameter

\frac {1}{4}

. It is sharpened perfectly so that it remains

8

inches long, with a

7

inch section still cylindrical and the remaining

1

inch giving a conical tip. What is its volume?

geometry3D geometry