Write one or more inequalities that describe the set of points.
-The interior of the sphere $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } = 36$
A) $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } \leq 36$
B) $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } \leq 6$
C) $x ^ { 2 } + y ^ { 2 } + x ^ { 2 }

Question

Write one or more inequalities that describe the set of points.
-The interior of the sphere $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } = 36$
A) $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } \leq 36$
B) $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } \leq 6$
C) $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } < 36$
D) $x ^ { 2 } + y ^ { 2 } + x ^ { 2 } < 6$

Quizplus · Accepted Answer

The sphere represents all points in 3D space that have a distance of exactly 6 units from the origin. Therefore, the interior of the sphere would be all points that have a distance less than 6 units from the origin. This can be represented by the inequality:
$$x^2+y^2+z^2<36$$
or, in this case,
$$x^2+y^2+x^2<36$$
Option C is the only inequality that indicates points strictly inside the sphere.

Write One or More Inequalities That Describe the Set of Points