Math Playground

Geometry

3D shapes & volume

Stretch a cube, swell a sphere, lift a cylinder. Watch volume and surface area follow your every move.

4
3
5
Formula
V = l × w × h
4 × 3 × 5 = 60
Volume
60
Surface area
94

Volume tells you how much space a 3D shape takes up. Each shape has its own formula — but they all reduce to the same idea: multiply a base area by some kind of height.

Cube / cuboid
V = l × w × h

Three perpendicular sides multiplied together.

Sphere
V = ⁴⁄₃ π r³

All you need is the radius.

Cylinder
V = π r² h

Circle area × height.

Cone
V = ⅓ π r² h

A cone is exactly one-third of a cylinder with the same base and height.

A sphere fits exactly two-thirds of the cylinder it's inscribed in. Archimedes was so proud of this result he asked for it on his tombstone.