# BASE CONE CONSTRUCTION

The base cone is a surface of revolution and so, construction of the base cone is similar to that of the main cone and uses the same side-elevation. This cone also is truncated. Let y be the height of the complete cone, a quantity needed in order to find its equation.

The base cone has a different base radius and vertex height than the main cone. The base cone is a cone that is truncated at height 1.70 cm. At this height, the radius must match the radius of the main cone, which is computed to be 5.38 cm. Its base radius is the same radius needed to construct triangle layer 1, and is 5.97 cm.

As a result, another equation of proportions is set up to find the total height:

 y5.97 = y - 1.705.38

5.38y = 5.97(y - 1.70)

y = 17.20

Now, let r be the radius of this cone at any given height v. Since one knows the total height, the same proportions that are set up for the main cone can be used here:

 5.9717.20 = r17.20 - v

17.20r = 5.97(17.20 - v)

r = 5.97 - .35v

Thus, the equation for the base cone becomes

BaseCone(u,v) = ((5.97 - .35v)cosu, (5.97 - .35v)sinu, v)

where u varies from 0 to 2pi and v from 0.00 to 1.70.

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