# Finding the volume of a Cube and a Cylinder

## Finding the volume of a Cube

### The formula for volume of a Cube

**Volume = s^3 s = side of cube**

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

**Solution =** 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 cube into two 45 degree angles. See below.

**Step 3.** You can apply the 45-45-90 rules in order to find the side length.side length will equal Hypotenuse / √2 = 6/√2

**Step 4.** Rationalize. =

**Step 5a.** Now I just need to cube the side (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**

## Finding the Volume of a Cylinder

#### Formula for Volume of a Cylinder = πr^(2 )* h

The πr^(2 ) =

**area of the base****h**= the height

**Problem 3**

**Find the volume of the cylinder that has a diameter of 6 units and a height of 8 units**

**Step 1**Find the radius by dividing the diameter in half.

6 /2 = 3 units which is r or the radius

**Step 2**. Plug the radius into πr^(2 ) which equals π3^(2 )

9π = base area of the cylinder

**Step 3**. 9π * height which equals 9π * 8 = 72π units^3 (remember volume is cubed)