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Finding the Volume of a Cube

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
5 x5 cube

How to find the volume of a cube


Hi welcome to MooMooMath. Today we are going to look at the volume of a cube. Over here we have a cube and a cube is like the Rubik’s cube, it has 6 side, 6 faces, and 4 sides on the base and they are all equal. This cube has sides of 5. This is a prism so we will look at the prism formula and simplify it down to make it specific to the cube. The base area of a prism times the height gives us the volume, so we need to find the area of the base. The base is just a square of 5 so 5 times 5 equals a base area of 25. So I will plug a twenty five in four base area. I will multiple it by the height of the cube, which is 5, so 5 (the height) times 25(the area of a base) is 125 and since this is volume it is units cubed because it is three dimensional. Now let’s simplify this down because we do have a special case. We have a cube that all sides are the same length. Since we have to find the base area and the height and they are all the same we can simplify that to S times S for the base area times S for the height or S cubed. So that is how you find the volume of a cube. So let’s review the rules for the volume of a cube it will be S times S times S or S cubed the units will also be cubed so let’s add that .It is derived from the prism formula which is base area time’s height to get the volume. The base area of a square is S times S times the height which is also S gives us the volume of a cube. Hope this video was helpful in finding the volume of a cube.

5
5
5
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
Cube 1
​Problem 2. This problem is slightly more challenging.

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




volume of a cube
90 degree angle cut in half by diagonal
45
45
6
6 x6 cube
arrow
rationalize 6/square root 2
Step 5b.  3*3*3 *√2*√2*√2 = 27*2√2

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


​Step 2. Use your 45-45-90 triangle rules to find the length of one side.
Step 1. The diagonal cuts the cube into two 45 degree angles.
The length of the hypotenuse equals leg length√2
The length of one leg of a 45-45-90 triangle equals hypotenuse/√2
arrrow pointing right

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

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.