**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.

****** 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

**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

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