In this publication, we will consider how to find the radius of a sphere circumscribed about a cone, as well as its surface area and the volume of a ball bounded by this sphere.
Finding the radius of a sphere/ball
Any one can be described. In other words, a cone can be inscribed in any sphere.
To find the radius of a sphere (ball) circumscribed about a cone, we draw an axial section of the cone. As a result, we get an isosceles triangle (in our case – ABC), around which a circle with radius r.
Cone base radius (R) equal to half the base of the triangle (B.C), and generators (l) – its sides (AB и BC).
Radius of a circle (r)circumscribed around a triangle ABC, among other things, is the radius of the ball circumscribed about the cone. It is found according to the following formulas:
1. Through the generatrix and the radius of the base of the cone:
2. Through the height and radius of the base of the cone
Height (h) a cone is a segment BE in the pictures above.
Formulas for the area and volume of a sphere/ball
Knowing the radius (r) you can find the surface area (S) spheres and volume (V) sphere bounded by this sphere:
Note: π rounded equals 3,14.