a circular cylinder is inscribed in a circular cone of a radius r and height h. what relation must hold between the radius and height of the cylinder?hello, i got this problem in my book titled...

a circular cylinder is inscribed in a circular cone of a radius r and height h. what relation must hold between the radius and height of the cylinder?hello, i got this problem in my book titled "analytic geometry" by love rainville chapter 5:"the straight line",page 64 exercise number 20 and the topic was all about the "intercept form". hope you could help me.

Asked on by eng-bryan

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neela | High School Teacher | (Level 3) Valedictorian

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Let h and r  be the height and radius of the cone.of the cone, and x be the semivertical  angle of the cone.

Let be the a be the radius of the cylinder and h1 be the height of the cylinder. Then the cylinder's top surface is a circle of radius a. The height of the above the cylinder is h-h1.

Noe a and  h -h1 has the relation (h-h1 )tanx = a....(1).

Also the radius of the cone and height of the cone has the relation :

h tanx = r.....(2):

From (1) and (2) we get:

We eliminate tan x between (1) and (2) by the operation (1)/(2):

(h-h1)/h = a/r.

 Therefore a = (h-h1)r/h

Or radiusof the cylinder = (Height of cone - height of cylinder)(radius of cone)/height of cone.

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