What region of $\mathbb { R } ^ { 3 }$ is represented by the inequality $x ^ { 2 } + y ^ { 2 } \leq 1$ ?
A)points inside a circular cylinder with axis the x-axis
B)points inside a circular cylinder with axis the y-axis
C)points inside a circular cylinder with axis the z-axis
D)points inside a sphere of radius 1
E)points inside a sphere of radius $\sqrt { 2 }$
F)points inside a sphere of radius 2
G)points inside a sphere of radius $\sqrt { 3 }$
H)points inside a sphere of radius 3

Question

What region of $\mathbb { R } ^ { 3 }$ is represented by the inequality $x ^ { 2 } + y ^ { 2 } \leq 1$ ?
A)points inside a circular cylinder with axis the x-axis
B)points inside a circular cylinder with axis the y-axis
C)points inside a circular cylinder with axis the z-axis
D)points inside a sphere of radius 1
E)points inside a sphere of radius $\sqrt { 2 }$ 
F)points inside a sphere of radius 2
G)points inside a sphere of radius $\sqrt { 3 }$ 
H)points inside a sphere of radius 3

Quizplus · Accepted Answer

The inequality $x^2 + y^2 \leq 1$ describes all points in $\mathbb{R}^3$ whose distance from the z-axis is less than or equal to 1, forming a circular cylinder with radius 1 and axis along the z-axis.

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