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solmaris [256]
3 years ago
9

Find the volume of the solid bounded by the sphere x^2+y^2+z^2=2z

Mathematics
1 answer:
liraira [26]3 years ago
8 0
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

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

V=\dfrac43\pi r^3

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