# Conical Section

## Homework Statement

Suppose there is a Conical section (of a right circular cone) of total height 'l' and radii 'a' and 'b' (a>b). How do we derive the formula for the radius at a height 'h' (h<l) ?

## The Attempt at a Solution

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Draw a cross section through the middle and look for similar triangles whose properties you can use to solve your problem. (I think you are describing a frustrated cone, not a pure cone?)

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Mark44
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Draw a cross section through the middle and look for similar triangles whose properties you can use to solve your problem. (I think you are describing a frustrated cone, not a pure cone?)
Good advice, but the term is "frustum of a cone."

Good advice, but the term is "frustum of a cone."
Haha :rofl: (or in other words, a truncated cone)
How was his advice good? We can't use similar triangle property to find the radius.

Mark44
Mentor
Extend the vertical line at the center and the outer sloped line up until they meet, then you'll have similar triangles.

Forget the 3 dimensional aspect; it would be easier to think of a trapezoid with one side of length [itex]l[/tex], perpendicular to sides a & b. Call the remaining side c.

a & b still represent the upper and lower radii of your truncated cone, and r represents the radius of that object at height h above side a.

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Extend the vertical line at the center and the outer sloped line up until they meet, then you'll have similar triangles.
I find the algebra easier if you construct the additional 2 line segments shown in the attached drawing.

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Thanks alot zgozvrm. I got my answer