A toy is constructed by joining a hemisphere to a cone by their plane faces. Both the

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A toy is constructed by joining a hemisphere to a cone by their plane faces. Both the hemisphere and cone have the same radius, r, and the cone has height. 10r. Given that the density of the cone is ρ, and that the density of the hemisphere is kρ, find the value of k such that the toy can balance when the joint face is vertical.

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