Find the center of mass of the solid cone bounded by the surface z = 4-√√x² + y² and z=0 with the density function p(x, y, z) = 8 - z Hint use symmetry to conclude the center of mass must be on the z-axis, and use integration to find the z-coordinate of the center of mass. Use cylindrical coordinates for the integration. 8₂ 9₂ (8) h₂ (rcos(8),rsin(8)) S & g₁(8) h, (rcos(8),rsin()) ffff(x, y, z) dv = S f(r cos(8),r sin(0),z) r dz dr de Write final answer in exact form, not a decimal approximation.

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Find the center of mass of the solid cone bounded by the surface

z = 4 - x^{2} + y^{2}

and

z = 0

with the density function

ρ (x, y, z) = 8 - z

Hint use symmetry to conclude the center of mass must be on the z-axis, and use integration to find the z-coordinate of the center of mass. Use cylindrical coordinates for the integration.

∭_{Q} f (x, y, z) d V = \int_{θ_{1}}^{θ_{2}} \int_{g_{1} (θ)}^{g_{2} (θ) h_{2} (r c o s (θ) \cdot c o s (θ), r s i n (θ))} f (r cos (θ), r sin (θ), z) r d z d r d θ

Write final answer in exact form, not a decimal approximation.

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