Search

# 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

= 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)