How to Calculate the Vertices of a Cone
A cone really has no vertices because a cone has no edges, but it does have a vertex, which is the point where the surface of the cone ends. Generally, a cone refers to a right circular cone which is one created by all lines drawn from a circular base and terminating at a common point called the vertex, such that a perpendicular line drawn from the vertex to the center of the base is called the height of the cone. If a right cone is viewed from a side cut, an isosceles triangle can be seen and half of that creates a right triangle. An isosceles triangle allows you to utilize the Pythagorean theorem to find the height to the vertex of a right circular cone.An oblique circular cone is one in which not all sides are equal in length, so the cone leans to one side and its vertex is off center. If an oblique cone is viewed from a side cut, an oblique triangle can be seen. An oblique triangle means that the Pythagorean theorem cannot be utilized to find the height to the vertex. Instead, trigonometry is used to find the answer.
- Difficulty:
- Moderately Easy
Instructions
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Right Circular Cone
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1
Draw the cone on paper and label the key parts. H is the height up to the vertex, which is what is you want to know. R is the radius.
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2
Write the known measurements on the drawing. (AB = 10 and BD = 5.)
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3
Write down the Pythagorean theorem.
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4
Replace the Pythagorean theorem terms with the line segment variables.
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5
Solve for the line segment AD squared.
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6
Plug in the known measurements.
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7
Solve the equation for AD squared.
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8
Solve the equation for AD by taking the square root of both sides. This is the answer.
Oblique Circular Cone
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1
Draw the cone on paper and label the key parts. H is the height up to the vertex, which is what is you want to know. R is the radius.
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2
Write the known measurements on the drawing. (AB = 10 and the angle of corner B = 65 degrees.)
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3
Write down the trigonometry equation.
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4
Plug in the known measurements.
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5
Solve the equation for AD. This is the answer.
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1
Tips & Warnings
A scientific calculator is required.
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- Photo Credit John Gugie
