Question

WRITE INEQUALITIE TO DESCRIBE A REGION CONSISTING OF ALL POINTS BETWEEN ( BUT NOT ON ) THE SPHERES OF RADIUS R AND r CENTERED AT THE ORIGIN. WHERE r

Answer 1

`r^2<x^2 + y^2+z^2 < R^2`

Explanation:

We are given the following in the question:

`r < R`

where r and r are the radius of the circle.

General equation of circle:

`(x-h)^2 + (y-k)^2 + (z-j)^2 = r^2`

where(h,k,j) is the center of the circle and r is the radius of circle.

If the circle is centered at origin, then,

`x^2 + y^2+z^2 = r^2`

Equation of circle with radius R centered on origin

`x^2 + y^2+z^2 = R^2`

Inequality to describe the region that consist of all points lying between the sphere of radius r and R but not on the sphere is given by:

`r^2<x^2 + y^2+z^2 < R^2`