 # Calculate Slope Of A Cone

## How To Calculate Slope Of A Cone

### Overview:

Helpful when you need to get the correct area of a turret, castle or other Medieval structure. In order to find the slope of a cone, you must first have the radius of the base of the cone. If you know the circumference of the circle, use the following calculation to get the radius.
A conical shape with a circumference of 60 feet.
60 = 3.14 × Diameter
Diameter = 60 ÷ 3.14
Diameter = 19.108

Now, if you take the diameter and divide it by two you will get the radius. 19.108 ÷ 2 = 9.554. Now, assuming you know the hypotenuse (rafter length or slope length) you can use the Pythagorean Theorem to find the height of the cone.

Example: A2 + B2 = C2
Where:
B = Height
C = Rafter or Slope Length From the above drawing this would work out as follows:
(9.554)2 + B2 = (12)2
91.28 + B2 = 144
B2 = 144 – 91.28
B2 = 52.72
B = 7.26 (which is the Height of the Cone)

Now we can use the rise over run to calculate the slope of the cone:
B = Rise (Height) = 7.26′
A = Run (Radius) = 9.55′

The slope could be left as 7.26, or if you want to see it over 12 then:
Rise ÷ Run -or- 7.26 ÷ 9.55 = .7602

Then take the Slope Ratio * 12 to find the slope:
Slope Ratio = .7602 * 12 = 9.12