Cone

A circle pulled to a point. Ice-cream, party hats, traffic markers.

A cone is a circle that's been pulled to a single point. Ice-cream cones, party hats, traffic markers and rocket nose-cones all share this shape.

Try this

radius r (height = 10)

volume = 1/3·π·r²·10 = 167.55

Volume

V = \frac{1}{3} π r^{2} h

Exactly one-third of the cylinder it'd fit inside.

Surface area

A = π r^{2} + π r ℓ

ℓ is the slant height (from apex to edge of base).

Try this: fill a cone with water and pour it into a cylinder of the same base and height. It takes exactly three cones to fill the cylinder.