- #1
whereisnomar
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Homework Statement
Find the centroid of the hemisphere, z=sqrt(a-x^2-y^2).
Homework Equations
z(bar)=(1/m)* Surface integral(z dS)
dS= magnitude of the magnitude of normal vector * dA
The Attempt at a Solution
I use the gradient to the hemisphere to get the magnitude of the normal vector... which comes out to be 2a. But the book says to use the cross product of the partial derivatives of a parametrization of the function as a parametric surface. And I get the wrong answer when I use the gradient.
Why can't you use the gradient to get the normal needed for a surface integral?