Content

• Steps
• Part 1 of 2: How to find the edge of a cube
• Part 2 of 2: How to Calculate the Volume of a Cube
• What do you need

The volume of a three-dimensional figure is a quantity that characterizes the space occupied by that figure. The volume is equal to the product of the length of the figure by its width and height. A cube is a three-dimensional shape that has the same length, width, and height, that is, all the edges of the cube are equal. Therefore, it is quite easy to calculate the volume of a cube if you know the value of its edge. And an edge can be found by the surface area of ​​a cube.

Steps

Part 1 of 2: How to find the edge of a cube

1. 1 Write down a formula for calculating the surface area of ​​a cube. The formula looks like this: ${ displaystyle S = 6x ^ {2}}$, where ${ displaystyle x}$ - the edge of the cube.
   • To calculate the volume of a cube, you need to multiply the values ​​of its three edges (length, width and height).A cube has the same length, width and height, so you need to find the value of one (any) edge to calculate the volume of the cube. Keep in mind that to calculate the surface area of ​​a cube, you need to know the value of the edge; therefore, if the surface area of ​​a cube is given, you can easily find its edge, and then calculate the volume of the cube.
2. 2 Plug the surface area of ​​the cube into the formula. Surface area must be given in the problem.
   • If the surface area of ​​the cube is unknown, do not use this method.
   • If a cube edge value is given, ignore the following steps and substitute that value (instead of ${ displaystyle x}$) into the formula for calculating the volume of a cube: ${ displaystyle V = x ^ {3}}$.
   • For example, if the surface area of ​​a cube is 96 cm, the formula will be written as follows:
     ${ displaystyle 96 ^ {2} = 6x ^ {2}}$
3. 3 Divide the surface area of ​​the cube by 6. This is how you find the meaning ${ displaystyle x ^ {2}}$.
   • For example, if the surface area of ​​a cube is 96 cm, divide 96 by 6:
     ${ displaystyle 96 ^ {2} = 6x ^ {2}}$
     ${ displaystyle { frac {96} {6}} = { frac {6x ^ {2}} {6}}}$
     ${ displaystyle 16 = x ^ {2}}$
4. 4 Extract the square root. This is how you find the meaning ${ displaystyle x}$, that is, the value of the edge of the cube.
   • The square root can be extracted with a calculator or manually. If you are unsure how to manually extract the square root, read this article.
   • In our example: ${ displaystyle 16 = x ^ {2}}$, that is, you need to extract the square root of 16:
     ${ displaystyle 16 = x ^ {2}}$
     ${ displaystyle { sqrt {16}} = { sqrt {x ^ {2}}}}$
     ${ displaystyle 4 = x}$
     Thus, the edge of a cube, whose surface area is 96 cm, is 4 cm.

Part 2 of 2: How to Calculate the Volume of a Cube

1. 1 Write down the formula for calculating the volume of a cube. The formula looks like this: ${ displaystyle V = x ^ {3}}$, where ${ displaystyle V}$ - the volume of the cube, ${ displaystyle x}$ - the edge of the cube.
2. 2 Plug the edge of the cube into the formula. You find this value from the known surface area of ​​the cube.
   • For example, if the edge of a cube is 4 cm, the formula will be written like this:
     ${ displaystyle V = 4 ^ {3}}$.
3. 3 Cube (third power) the edge of the cube. Do this on a calculator, or simply multiply x by yourself three times. This will find the volume of the cube in cubic units.
   • For example, if the edge of a cube is 4 cm, the calculations will be written like this:
     ${ displaystyle V = 4 ^ {3}}$
     ${ displaystyle V = 4 times 4 times 4}$
     ${ displaystyle V = 64}$
     Thus, the volume of a cube, the edge of which is 4 cm, will be 64 cm.

What do you need

• Pencil pen
• Paper