Answer to Question #160269 in Analytic Geometry for Priya

Question

Show that the closed sphere with centre (7,3,2)and radius 10 in R³ is contained in the open cube P = {(x, y,z ):|x − 2 |<11,|y− 3|<11, |z − 7 |<11}.

Answer 1

The equation of the sphere is: $(x-7)^2+(y-3)^2+(z-2)^2=10^2$. We point out that the point with coordinates $(17,3,2)$ belongs to the sphere. However, the point is not contained in the cube, since $|17-2|=15>11$. Thus, the sphere is not contained in in the cube.