olymmath

HMMT 2019 U27

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Consider the eighth-sphere {(x,y,z)∣x,y,z≥0,x2+y2+z2=1}\left\{(x, y, z) \mid x, y, z \geq 0, x^{2}+y^{2}+z^{2}=1\right\}. What is the area of its projection onto the plane x+y+z=1x+y+z=1 ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{\pi \sqrt{3}}{4}

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