Surface Area & Volume Formulas

A prism can be described as a stack of shapes. The figure shows a prism of triangles stacked d thick, but any shape could be used.

Surface area = 2A + Pd

where
A = area of the base shape
P = perimeter of base shape
d = height of prism

Volume = Ad

A cylinder is a prism with a circular base.

Surface Area = 2πr² + 2πrh
Volume = πr²h

A sphere is a shape where the distance from the center to the edge is the same in all directions. This distance is called the radius ( r ).

Surface area = 4πr²
Volume = 4/3πr³

A pyramid is a solid figure with a polygonal base and triangular faces that meet at a common point over the center of the base.
The height ( h ) is the distance from the base to the apex or top of the pyramid.
The side length ( s ) is the height of the face triangles.
The perimeter ( P ) and the area ( A ) of the base is calculated according to the shape of the base.

Surface Area = ( ½ x P x s ) + A
Volume = 1/3 Ah

The figure shows a pyramid with a square base ( a = b ) with equalateral triangles for faces.

Surface area = a² + √3( a² )
Volume = √5(a³/6)

A cone is a pyramid with a circular base of radius ( r ) and the side length ( s ) is the length of the side.

s = √( r² + h² )

Surface Area = πr² + π( r x s )
Volume = 1/3( πr²h )