Word Count : 294

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We are asked to evaluate [ \iiint_S z^2 , dx,dy,dz ] where (S) is the solid region between the spheres (\rho = 1) and (\rho = 2). We will solve this using spherical coordinates. --- In spherical coordinates: [ x = \rho \sin\phi \cos\theta, \quad y = \rho \sin\phi \sin\theta, \quad z = \rho \cos\phi ] and the volume element is: [ dx,dy,dz = \rho^2 \sin\phi , d\rho, d\phi, d\theta ] Also, (z^2 _________ _______ ___ ________ ___.
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