Step 1: Picture the pencil as two pieces joined together.
Think of an unsharpened pencil, it is just a long cylinder with a circular cross-section throughout. Nothing tricky there.
Step 2: Look at what sharpening does.
When you sharpen one end, wood is shaved away evenly all around, so the flat circular end tapers smoothly down to a single point. A surface that starts as a circle and narrows down to a point while moving along an axis is exactly what we call a cone.
Step 3: Put the two pieces together.
So the body of the pencil stays a cylinder, and the sharpened tip becomes a cone sitting on top of it, sharing the same circular base. \[ \boxed{\text{A Cone and a Cylinder}} \]