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# How to find the volume of a cube

### Volume Formula for a cube equals: Base Area * Height | Ba * h

cube is a three dimensional shape that has six equal sides. The volume is found by using the following formula

The Base Area  of a cube = Length * Width

Example problem from video

Find the volume of cube 1 that has
sides of 5 units.

Step 1 Find the base area
Length * Width
5 * 5 = 25

Step 2 Multiple base area * height
25 * 5 = 125 units^3
Because all the sides of a cube are equal you can also find the volume of a cube by cubing one side.

Formula for volume of a cube = Side^3

5^3 = 125 units ^3

Problem 2. This problem is slightly more challenging.

Find the volume of a cube with a diagonal length of 6 units

Step 1. The diagonal cuts the cube into two 45 degree angles.

Step 2. Use your 45-45-90 triangle rules to find the length of one side.

The length of the hypotenuse equals leg length√2
The length of one leg of a 45-45-90 triangle equals hypotenuse/√2

Step 3.   Because you have the hypotenuse length you can find the side length by dividing hypotenuse/ √2 = 6/√2

Step 4.   Rationalize.

Step 5a. Plug the side length into the volume formula “side^3”  which becomes (3√2 )^3 = 3*3*3 *√2*√2*√2

Step 5b.  3*3*3 *√2*√2*√2 = 27*2√2

Step 6.    Volume of Cube   27*2√2 = 54√(2 ) units^3

## Related Sites...

Cubes/Illuminations   Use this interactive cube creator to help understand the volume of a cube, You can also calculate the volume of different cubes, and it will check your work.

Calculating the volume of a Cube/WikiHow  Step by step directions for calculating the volume of a cube with pictures.

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