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I'm stuck on this question and not sure how to approach it.

A metallic surface S is in the shape of a hemisphere

$z$=$\sqrt{R^2-x^2-y^2}$ ,$0\leq x^2$+$y^2$$\leq R^2$

if the mass density of the metal per unit area is given by $m(x,y,z)$=$x^2$+$y^2$ Find the total mass of S.

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Total mass of S is given by $$\mathrm{ \iint_{S}m\;\color{blue}{dS}} $$ Using spherical coordinates (physics convension) this integral can be written as $$\mathrm{ \int_0^{2\pi}\int_0^{\pi\over2} R^2\sin^2\theta\;\color{blue}{R^2\sin\theta\;d\theta\;d\phi}=\frac{4}{3}\pi R^4 }$$

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