Finding the volume of a Cone given the slant height

           Finding the Volume of a Cone given the Slant Height

 Here is the video that works the volume of a cone using the slant height

Problem 1 Find the volume of a cone with a slant height of 9 units and a diameter of 12 units.

 

 

 

 

 

 

Step 1 Find the radius by taking ½ of the diameter

  ½ * 12 =6 units

 

Step 2 Notice that the slant height is part of a right triangle. We need the height to figure out the volume. The formula for volume = πr^2*h

 

 

 

 

 

 

 

Step 3. We can use the Pythagorean Theorem to find the height.

The radius becomes the leg of the right triangle

The slant height becomes the hypotenuse of the right triangle

So for the height I will use a^2+ 6^2= 9^2

Step 3a a^2+ 36= 81 

 

Step 3b a^2= 45  

 

Step 3c  a= √(45 ) this simplifies to 3√5 

 

Step 4 So now use the volume formula πr^2*h 

 

Step 4a  π6^2*3√5

 

Step 4b  36π* 3√5 

 

Step 4c 108√5 π units^3 is the volume

Finding the volume of a cone

The formula for the volume of a cone = 1⁄3 πr^2*h

h =height

r = radius

 Please note πr^2*h is actually the volume of a cylinder that has the same height and radius. However it takes three cones to fill up a cylinder so that is why you multiply by 1/3

 Video for Volume of a Cone

Problem 1. Find the volume of a cone with a height of 10 and a radius of 6 units.

 

 Click the cone above for additional information

Step 1.  Plug your numbers into the formula. 

              1⁄3 π6^2*10  

 

Step 2 Simplify 1⁄3 π6^2*10  

 

Step 2b 1⁄3 π36*10

 

Step 3 1⁄3 x 36⁄1 π x 10  

 

Step 3b 12π x 10=120π units^3 (Please note volume is always cubed)