- #1

richies

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## Homework Statement

Find the center of mass of the solid figure similar to a cone pointing upward with slope = 1

Note: the density varies with z^2 and the edge has a slope of 1. From symmetry we see that both Xc and Yc are equal to zero. Find the center of mass in the z direction as a function of h by doing the appropriate integral.

## Homework Equations

p(vector r) = z^2 z^

slope = 1

## The Attempt at a Solution

I'm thinking about using cylindrical coordinates

@ radius = sqrt of (1 - h^2)

@ Z = 1/V ∫ z dV (lower limit V)

@ V = 1/3*pi*r^2*h

@ dV = r⊥dr⊥dθ dz.

@ ∫ z dV (lower limit V) = ∫ (∫ (∫zr⊥dr⊥) dθ) dz

Now I am stuck there i don't know if I am doing it right or wrong.

Any help or idea ?

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