Topic Sections

## Surface area and volume

Surface area

The surface area is simply the area of all of the outside surfaces of a three-dimensional object.

So the surface area of a cuboid is calculated from adding together the area of all six faces.

The surface area of a cube can be calulated from the formula

$\dpi{100}&space;SA&space;=&space;6x^{2}$

where  SA = surface area    and     x = the length of the square faces.

An understanding of surface area is important to the chemist because chemical reactions occur between particles on the surface of the bulk of mass. Therefore the surface area of a sphere is of interest to the chemist, making the assumption that particles are spherical in shape.

The surface area of a sphere is calculated from the formula

$\dpi{100}&space;SA=4\pi&space;r^{2}$

where  SA = surface area   and   r = the radius of the sphere.

The size of the surface area plays an important role in determining the rate of a chemical reaction. The larger the surface area, the faster the rate of reaction.

Volume

The volume of a three-dimensional figure is the amount of space within it. That is, the volume of a polyhedron is equal to the number of unit cubes that can fit inside it. Sometimes determining the number of cubes that will fit is easy, and sometimes it's rather difficult - depending on the actual shape!

The volume of a cuboid is calculated from the formula

$\dpi{100}&space;V&space;=&space;l\times&space;b\times&space;h$

where   V = volume,   l = length,   b = breadth    and   h = height.

The volume of a sphere is calculated from the formula

$\dpi{100}&space;V&space;=&space;\frac{4}{3}\pi&space;r^{3}$

where   V = volume    and   r = radius of the sphere.

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