Finding the volume of a Cone given the slant height

Tuesday, June 11, 2013

Finding the Volume of a Cone given the Slant Height

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

volume of a cone

**** Each step described below is worked out in the video ****

Step 1. Find the radius by taking ½ of the diameter
 1 / 2 * 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, and the slant height becomes the hypotenuse of the right triangle.
So for the height, I will use a^2+ 6^2= 9^2

Pythagorean theorem

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.  Solution:  Volume = 108√5 π units^3

Related Links

Volume of a Cylinder


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