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MathNet 2019-part-08 — 179 problems (EN–VI) Question 109

Math Olympiad Vault · MathNet 2019-part-08 — 179 problems (EN–VI)

Question 109

Consider the eighth-sphere $\{(x, y, z) \mid x, y, z \geq 0, x^{2}+y^{2}+z^{2}=1\}$. What is the area of its projection onto the plane $x+y+z=1$?