# Geometry » Solids

## Cube

Area = 6 × s2 (s is the length of the side/edge)
Volume = s3

## Cuboid

Area = 2 × (l × w + l × h + w × h)
Volume = l × w × h

## Sphere

Area = 4 × π × r2
Volume = 43 × π × r3

## Cone

 Area cone = area base + area slanted face = π × r2 + π × r ×
 Volume = 13 × area base × height = 13 × π × r2 × h

## Prism

A prism consists of a polygon as a base and top. All cross-section, parallel to the base, must be identical.
Area = calculate faces separately and add them together
Volume = area base × height

## Pyramid

A pyramid consists of a polygon as a base and triangular slanted sides from every side of the polygon towards a common point/top.
Area = area slanted faces + area base
Volume = 13  × area base × height

## Cylinder

A cylinder consists of a circle or an ellipse as a base and top. All cross-sections, parallel to the base, must be identical.

### Formulas for circular base

 Area = area top and base + area side = 2 × area base + circumference base × height = 2 × π × r 2 + 2 × r × π × h
 Volume = area base × height = π × r 2 × h

### Formulas for ellipsoidal base

 Area = area top and base + area side = 2 × area base + circumference base* × height = 2 × π × r 2 + π × h
 Volume = area base × height = π × a × b × h

with a half the size of the longest axis and b half the size of the shortest axis

* The circumference formula of the ellips (circumference = π) is not precise.
A slightly more precise approximation is circumference = π(3(a + b) – )
Only with a very difficult calculation (ellipsoidal integral) can the circumference of a ellips be calculated precisely.