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.