An idealized hourglass is made by joining two identical circular cones, each with base radius \(...

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An idealized hourglass is made by joining two identical circular cones, each with base radius \( 12 \mathrm{~cm} \) and height 18 \( \mathrm{cm} \), at their vertices, A tiny hole allows water to drop from the upper cone into the lower one. At a certain instant, the depth of water in the upper cone is \( 6 \mathrm{~cm} \) which is decreasing at a rate of \( 0.2 \mathrm{~cm} / \mathrm{min} \), and water in the lower cone is 10 \( \mathrm{cm} \) deep. Find the rate of increase of depth of water in lower cone.
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