Irregular Cone Geometry Problem: Finding the Area of an Elliptical Base

In summary, the conversation discusses the possibility of finding the area of the base of an elliptical, non-right cone using known parameters such as the length from the center of the ellipse to the vertex and the angle of the sides. The suggested solution involves slicing the cone to create a circular cross-section and using trigonometry to find the area of the projection.
  • #1
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Homework Statement



I'm wondering whether or not it is possible to get the area of the base of an elliptical, non-right cone if the following two parameters are known:

- length from center of ellipse up to vertex
- angle that the sides make

Here is a simple visual: http://i.imgur.com/M6jT5.png

Homework Equations



[tex]A=\pi ab[/tex]

The Attempt at a Solution



I've tried looking at geometry guides with no success. I'm thinking I might be able to use some clever trig and drop a right angle down from the vertex in order to get the length of the semi-minor/major axis, but I can't reason it out. any advice would be appreciated.
 
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  • #2
Hi Appity! :smile:

Hint: slice the cone so that you get a circular cross-section, then use trig to find the area of the projection. :wink:
 

What is Irregular Cone Geometry?

Irregular Cone Geometry is a branch of mathematics that deals with the properties and measurements of cones that do not have a perfect circular base. Instead, the base of the cone may be an ellipse, parabola, or other irregular shape.

How is Irregular Cone Geometry different from Regular Cone Geometry?

The main difference between Irregular Cone Geometry and Regular Cone Geometry is the shape of the base. In Regular Cone Geometry, the base is always a perfect circle, while in Irregular Cone Geometry, the base can be any irregular shape.

What are some real-world applications of Irregular Cone Geometry?

Irregular Cone Geometry has many applications in various fields, such as architecture, engineering, and physics. It is used to design structures such as roofs, bridges, and buildings. It also plays a role in calculating the volume and surface area of irregularly shaped objects in physics and chemistry.

How is the volume of an irregular cone calculated?

The volume of an irregular cone is calculated by finding the area of the base and multiplying it by the height of the cone. The formula for calculating the volume is V = 1/3 * π * r^2 * h, where r is the radius of the base and h is the height of the cone.

What are some common misconceptions about Irregular Cone Geometry?

One common misconception about Irregular Cone Geometry is that all cones have a perfect circular base. However, this is not true, as cones with other base shapes also fall under this category. Another misconception is that the volume of an irregular cone is always smaller than a regular cone, but this depends on the specific measurements of each cone.

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