Finding the Volume of a Cube

The formula for the volume of a cube equals one side raised to the third power.

Volume = s^3

Problem 1 What is the volume of a cube with a side length of 3 units?

Step 1 3*3*3 or 3^3 = 27 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. Use your 45-45-90 rules of a triangle to find the length of one side.

Step 2. The diagonal cuts the side of the cube into two 45 degree angles. See below.

Step 3. The side length will equal Hypotenuse √2 = 6√2

Step 4 Rationalize. 6/√2 * √2/√2 = (6√2)/2 =3√2 = one side

Step 5 Now I just need to cube the side (3√2 )^3 = 3*3*3 *√2*√2*√2

3*3*3 *√2*√2*√2 = 27*2√2

27*2√2 = 54√(2 ) units^3

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