What is the equation of the sphere with unit radius having centre at the origin?

x^{2} + y^{2} + z^{2} = 0

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x^{2} + y^{2} + z^{2} = 1

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x^{2} + y^{2} + z^{2} = 2

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x^{2} + y^{2} + z^{2} = 3

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Solution

The correct option is B $x^{2} + y^{2} + z^{2} = 1$
Equation of circle having center at $(a, b, c)$ and radius $r$ is $\sqrt{{(x - a)}^{2} + {(y - b)}^{2} + {(z - c)}^{2}} = r$
Radius is $r = 1$ and center is $(0, 0, 0)$
So, the equation will be $\sqrt{x^{2} + y^{2} + z^{2}} = 1$
$\Rightarrow x^{2} + y^{2} + z^{2} = 1$

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