Math CentralQuandaries & Queries


Question from Jack:

I need to build a truncated cone that has a top of 30 inches and a base of 64 inches . The sides need to be at a 64.5 degree angle. This will determine the height. Can this be calculated?

i Jack,

I drew a diagram of your truncated cone and drew a line from $B$ to intersect the base at $C.$ The length of the line segment $BC$ is $h,$ the height in inches.

truncated cone

Since the radius of the top is $15$ inches and the radius of the base is $32$ inches the length of the line segment $CA$ is $32 - 15 = 17$ inches and the measure of the angle $CAB$ is $65^{o}.$ Thus

\[\tan\left(65^o\right) = \frac{h}{|CA|}\]


\[h = 17 \times \tan\left(65^o\right) \mbox{ inches.}\]


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