sphere

Question

The equation of sphere with center at origin and radius r is

RankGuru · Accepted Answer

1. **Definition**: A sphere is the locus of a point $(x, y, z)$ whose distance from a fixed point (center) is constant (radius $r$).
2. **Distance Formula**: Distance from $(x, y, z)$ to $(0, 0, 0)$ is $\sqrt{x^2 + y^2 + z^2}$.
3. **Equation**: Set distance equal to $r$: $\sqrt{x^2 + y^2 + z^2} = r$.
4. **Simplification**: Squaring both sides: $x^2 + y^2 + z^2 = r^2$.

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