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