# How to find the volume of a cube

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

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

**Base Area**of a cube = Length * Width

**Step 1**Find the base area

**Step 2**Multiple base area * height

**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.

**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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