How To Draw A Truncated Cone Pattern

Pattern for a Truncated Cone:

First, call up near extending the conical effigy up to a point. That is, this pedestal is formed by cutting off a cone with a base of operations having a diameter of eight inches. The completed cone looks like the figure at the correct.

I have labeled a few lengths in the figure because they will be useful later.

The idea is to know the values of h, a, and b then gyre the effigy out flat.

Offset, h. We take h + 12 is the altitude of the whole cone and h is the altitude of the little cone. Now, we have like triangles and so

So, h = 6 -- that is the altitude of the piddling cone -- and the altitude of the large cone is eighteen.

By using the Pythagorean relation for the correct triangles, we can determine the lengths of the lateral sides of the cones and the pedestal.

And then

which is approximately seven.21 inches.

Then

So,

which is approximately 21.63 inches.

Therefore, b is approximately fourteen.42 inches.

At present, the pattern we want to lay out flat is cut from a circular disc of radius 21.63 inches and we remove a piece of a circular disc of radius 7.21 inches (the small cone). Like this:

What is left to make up one's mind is how big is the angle from A effectually to B to become the arc lengths and ?

In order to determine the angle nosotros employ the relation that the arc length S is given by

where r is the radius and the bending is in radians. We can ready this upward using either the modest circle or the large one. Using the small circle with radius of vii.21 and arc length of , we take

Therefore,

Multiply past the conversion factor to get degree measure out and you lot have:

This is a reflex angle slightly larger than a direct angle, every bit pictured in a higher place.

The same value for the angle can be found by using the arc length and the radius 21.63. Indeed, 21.63 = 3(7.21).

Now, to make the design, draw a circumvolve of radius 21.63 and a smaller circumvolve of radius vii.21. Marker off any radius, and then measure an angle of 200 degrees. Cut out the blue figure and join the two sides together.