How To Find The Volume Of A Cube From Its Surface Area 7 Steps

To find the volume of a cube, you need to multiply its three dimensions (length, width, height) together. [2] X Research source These dimensions correspond to the length of the edges of the cube. Since all the dimensions (edges) of a cube are the same, in order to find the volume of the cube, you first have to determine the length of one of its edges. Since finding the surface area of a cube also requires the length of one edge, if you know the surface area, you can work backwards to find the length of one edge, then use the edge length to work forward to find the volume.

If you do not know the surface area of the cube, this method will not work. If you already know the length of one edge of the cube, you can skip the following steps and plug in that value for x{\displaystyle x} into the volume of a cube formula: volume=x3{\displaystyle volume=x^{3}}. For example, if the surface area of your cube is 96 square centimeters, your formula will look like this:96cm2=6x2{\displaystyle 96cm^{2}=6x^{2}}

For example, if the surface area of your cube is 96 square centimeters, you would divide 96 by 6:96cm2=6x2{\displaystyle 96cm^{2}=6x^{2}}966=6x26{\displaystyle {\frac {96}{6}}={\frac {6x^{2}}{6}}}16=x2{\displaystyle 16=x^{2}}

You can find the square root using a calculator, or by hand. For complete instructions, read Calculate a Square Root by Hand. For example, if 16=x2{\displaystyle 16=x^{2}}, then you need to find the square root of 16:16=x2{\displaystyle 16=x^{2}}16=x2{\displaystyle {\sqrt {16}}={\sqrt {x^{2}}}}4=x{\displaystyle 4=x}So, the length of one edge for a cube with a surface area of 96cm2{\displaystyle 96cm^{2}} is 4cm{\displaystyle 4cm}.

For example, if one edge of a cube is 4 centimeters, then your formula will look like this:v=43{\displaystyle v=4^{3}}.

For example, if the length of one edge is 4 centimeters, you would calculate:v=43{\displaystyle v=4^{3}}v=4×4×4{\displaystyle v=4\times 4\times 4}v=64{\displaystyle v=64}So, the volume of a cube with an edge length of 4 centimeters is 64cm3{\displaystyle 64cm^{3}}