Difference between revisions of "Surface area"
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| − | The '''surface area''' of a solid is the total exposed [[area]] that it has. For example, the | + | The '''surface area''' of a solid is the total exposed [[area]] that it has. For example, the surface area of a [[cube]] is the sum of the areas of its six [[square]] [[face]]s; the surface area of a [[tetrahedron]] is the sum of the area of its four [[triangle | triangular]] faces. In general, for any [[polyhedron]] without holes, the surface area is just the sum of the areas of the faces of the polyhedron. Some other solids, such as the [[cylinder]] and [[right cone]], have surface areas that can be computed relatively easily. However, for most solids, [[calculus]] is necessary to compute the surface area. |
| + | For cubes, the surface area is <math>6s^2</math> | ||
| + | |||
| + | For a rectangular prism, the surface area is <math>2\cdot (lw+hw+lh)</math>, where l,w, and h are the length, width and height, respectively. | ||
| + | |||
| + | For spheres, the surface area is <math>4\pi \cdot r^2</math>. | ||
| + | |||
| + | For cylinders, the surface area is <math>2\pi \cdot rh+2\pi \cdot r^2</math>. | ||
| + | |||
| + | For cones, the surface area is <math>\pi \cdot r \cdot (r+\sqrt{h^2+r^2})</math> | ||
| + | |||
| + | For pyramids, the surface area is <math>lw+l \cdot \sqrt{(\frac{w}{2})^2+h^2}+w^2 \cdot \sqrt{(\frac{l}{2})^2+h^2}</math>. | ||
==See also== | ==See also== | ||
* [[Area]] | * [[Area]] | ||
* [[Volume]] | * [[Volume]] | ||
* [[Face]] | * [[Face]] | ||
Latest revision as of 00:34, 25 January 2016
This article is a stub. Help us out by expanding it.
The surface area of a solid is the total exposed area that it has. For example, the surface area of a cube is the sum of the areas of its six square faces; the surface area of a tetrahedron is the sum of the area of its four triangular faces. In general, for any polyhedron without holes, the surface area is just the sum of the areas of the faces of the polyhedron. Some other solids, such as the cylinder and right cone, have surface areas that can be computed relatively easily. However, for most solids, calculus is necessary to compute the surface area.
For cubes, the surface area is 
For a rectangular prism, the surface area is 
, where l,w, and h are the length, width and height, respectively.
For spheres, the surface area is 
.
For cylinders, the surface area is 
.
For cones, the surface area is 
For pyramids, the surface area is 
.
