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Multivariable Calculus

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Moderate

Centroid of Half Ball

MVCALC-Y7XKKV

Find the center of mass of the upper half ball:

$$B_u=\{(x,y,z): x^2+y^2+z^2\leq 1, z\geq 0\}$$

Assume $B_u$ has constant density.

A

$(0,0,\cfrac{1}{8})$

B

$(0,0,\cfrac{1}{4})$

C

$(0,0,\cfrac{3}{8})$

D

$(0,0,\cfrac{\pi}{6})$

E

$(0,0,\cfrac{\sqrt{2}}{4})$