MaKennaHenry8751 MaKennaHenry8751
  • 21-11-2017
  • Mathematics
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Find the volume of the solid bounded by the sphere x^2+y^2+z^2=2z

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LammettHash
LammettHash LammettHash
  • 21-11-2017
[tex]x^2+y^2+z^2=2z\implies x^2+y^2+z^2-2z+1=1\implies x^2+y^2+(z-1)^2=1[/tex]

is a sphere centered at (0, 0, 1) with radius 1. We only need to know the radius; the volume is

[tex]V=\dfrac43\pi r^3[/tex]

where [tex]r=1[/tex], so the volume would be [tex]\dfrac{4\pi}3[/tex].
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