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.