Answer to Question #107180 in Analytic Geometry for Nikesh gautam pandit ji

Question #107180
Show that the closed sphere with centre (2,3,7)and radius 10 in R^3 is contained in the open cube P = {(x, y,z): |x − 2 |<11, |y − 3| <11, |z − 7| <11}.
1
Expert's answer
2020-03-31T15:36:20-0400

Equation of the sphere with centre (2,3,7) and radius 10 in "R^3 \\implies (x-2)^2+(y-3)^2+(z-7)^2=10^2"

Thus, extremities of the sphere in all 3 directions can be found as :

"|x-2| <10, |y \u2212 3| <10, |z \u2212 7| <10" .


But the given cube is "P = \\{(x, y,z): |x \u2212 2 |<11, |y \u2212 3| <11, |z \u2212 7| <11\\}"

Thus, clearly the sphere lies inside the cube as its extremities are smaller than extremities of the cube!


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