Surface Areas

Surface Areas

Skip forward to main content

Cube: 6�( $s 2$ )

$s\,$ is the length of a side.

Rectangular Prism: 2�(( $l,$ � $w\,$ ) + ( $l\,$ � $h\,$ ) + ( $w\,$ � $h\,$ ))

$l\,$ , $w\,$ , and $h\,$ are the length, width, and height of the prism

Sphere: 4�π�( $r\,$ ²)

$r\,$ is the radius of the sphere

Cylinder: 2�π� $r\,$ �( $h\,$ + $r\,$ )

$r\,$ is the radius of the circular base, and $h\,$ is the height

Pyramid: $A = A_b + \frac{ps}{2}$

$A$ = Surface area, $A b$ = Area of the Base, $p$ = Perimeter of the base, $s$ = slant height.

The surface area of a regular pyramid can also be determined based only on the number of sides( $n$ ), the radius( $r$ ) or side length( $l$ ), and the height( $h$ )

If $r$ is known, $l$ is defined as $l = \sqrt{(rcos(\frac{360}{n})-r)^2 + (rsin(\frac{360}{n}))^2} = \sqrt{2}r\sqrt{1-cos(\frac{360}{n})}$

or if $l$ is known, $r$ is defined as $r = \frac{l}{\sqrt{2}\sqrt{1-cos(\frac{360}{n})}}$

The slant height $h 1$ is given by $\sqrt{r^2+h^2+\frac{l^2}{4}}$

The total surface area of the pyramid is given by $n\frac{l}{2}[h_1 + h_0]$

Cone: π�r�(r + √(r² + h²))

$r\,$ is the radius of the circular base, and $h\,$ is the height.

Extracted from http://en.wikibooks.org/wiki/Geometry. Reproduced under the GNU Free Documentation License

GMAT Tutorials

Surface Areas