Question: A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of (52mathrm{~cm}^{3}).

A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of $52\mathrm{~cm}^{3}$. If nickel plating costs $\$ 1$ per $\mathrm{cm}^{2}$ and silver plating costs $\$ 8$ per $\mathrm{cm}^{2}$, find the dimensions of the box to minimize the cost of the materials. (Use decimal notation. Give your answers to three decimal places.) len

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