Math CentralQuandaries & Queries

Question from Sameer:

Bottom cone radius 1124.hight is 200. Top radius 15degree decrease to bottom radius. Top radius how much ?


Below is my sketch the situation you described. My sketch is not to scale. $AB$ is the radius of the base circle so $|AB| = 1124$ units. The height $|AE| = |BD| = 200$ units and the radius $|EC|$ of the top circle is unknown. I'm going to call it $R$ units. The measure of the angle $BCD$ is 15 degrees.

truncated cone

The length of $ED$ is 1124 units so the length of $DC$ is $R - 1124$ units. The triangle $BCD$ is a right triangle and hence

\[ \tan(15^o) = \frac{|BD|}{|DC|} = \frac{200}{R-1124}.\]


\[R - 1124 = \frac{200}{\tan(15^o} = \frac{200}{0.2679} = 746.4.\]


\[R = 1124 + 746.4 = 1870.4 \mbox{ units.}\]


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