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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
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
8
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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Step 5b. 3*3*3 *√2*√2*√2 = 27*2√2
Step 6. Volume of Cube 27*2√2 = 54√(2 ) units^3