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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
volume of a cylinder

Finding the Volume of a Cylinder

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 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.  










Volume = s^3   s = side of cube


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


Finding the volume of a Cube and a Cylinder

volume of a cylinder
8
volume of a cube
volume of a cube
90 degree angle cut in half by diagonal
45
45
6

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 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) 



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Volume Surface Area Formulas

Volume Cube and Cylinder

Volume of a Cone

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 Cube

The formula for volume of a Cube

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