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Omni-MATH / Consider the eighth-sphere {(x,y,z)∣x,y,z≥0,x²+y²+z²=1}. What is the area of its projection onto the plane x+y+z=1 ?

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problem

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 ?
Plain-text mathematical notation (without MathML)
Consider the eighth-sphere {(x,y,z)∣x,y,z≥0,x²+y²+z²=1}. What is the area of its projection onto the plane x+y+z=1 ?
Original LaTeX notation
Consider the eighth-sphere $\left\{(x, y, z) \mid x, y, z \geq 0, x^{2}+y^{2}+z^{2}=1\right\}$. What is the area of its projection onto the plane $x+y+z=1$ ?

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Source and history

task_id
f4a1fe64-a441-580f-8a2a-da99163520b3
task_key
test--f4a1fe64-a441-580f-8a2a-da99163520b3
task_revision_id
1
config / split
/ test

Official source

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