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