A bowl in the form of a hemisphere of radius a is filled with glop that settles in such a way that its density at each point is proportional to the depth at that point. Find the mass of the glop.
Added by Samuel A.
Step 1
Let the radius of the hemisphere be \( a \). The density of the glop at a depth \( h \) from the surface is given by \( \rho(h) = k h \), where \( k \) is a proportionality constant. Show more…
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