University Multivariable Calculus: Surface Integrals:

Please help with details. Question copied below and also attached in the screenshot as well. Thanks.

Let S describe an empty bowl below the xy-plane, given by the equation

z = x^2 + y^2 - 1

and with density: density(x, y, z) = 5(x^2 + y^2) - z

a) What is the COM of the bowl?

b) If the bowl is filled with water of density 1, what is the COM of the bowl and water combo?

2) Let 3 describe an empty bow] below the xyplane, given by the equation z = m2 + y? 1 and with density 5(31913} = 5&2 +y2) z a) What is the COM of the bow]?I b) If the bow] is lled with water of density 1, what is the COM of the bowl and water combo