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# HALP ASAP

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A point in space $(x,y,z)$ is randomly selected so that $-1\le x \le 1$,$-1\le y \le 1$,$-1\le z \le 1$. What is the probability that $x^2+y^2+z^2\le 1$?

Apr 2, 2021

#1
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The probability is 1/6.

Apr 2, 2021
#2
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The equation $$x^2+y^2+z^2=1$$ represents a sphere with a center at (0, 0, 0) and a radius of 1, and the volume of the space that contains all the possible points of $$(x, y, z)$$ is a cube with a side length of 2. The volume of the sphere is $$\frac{4}{3}\pi$$, and the volume of the cube is $$8$$, so the probability that $$x^2+y^2+z^2\leq1$$ is $$\frac{\frac{4}{3}\pi}{8}=\boxed{\frac{\pi}{6}}$$

Apr 2, 2021