Unizor - Geometry3D - Final Problems 2

Unizor - Creative Minds through Art of Mathematics - Math4Teens

Notes to a video lecture on http://www.unizor.com

Geometry3D - Final Problem 2

Problem A
Find the radius r of a sphere inscribed into a right circular cone of altitude H and radius of a circular base R.

Answer
r = R·H ⁄ [R+√(R²+H²)]

Problem B
Two vertices at the base of an isosceles triangle lie on a circle at the base of a right circular cylinder, while the third vertex of this isosceles triangle lies on a cylinder's side surface.
The length of the base of a triangle is a=6, its altitude is h=2, angle between a plane where our triangle is located and the plane of the base of a cylinder is β=30o.
What is the radius R of a cylinder?

Answer
R = 2√3