Math CentralQuandaries & Queries


Question from Charles:

Sheet metal cone.
I need a cone with a finished base of 38.19719 diameter
The cone is to be from a 48 diameter round with the wedge cut out.
The best calculation I have is the arc is 286.479. (correct?)

Could you verify this arc angle but more so what is the cone height?

Hi Charles,

I agree with your calculation. The wedge to be removed sits on an arc of length 286.479 (inches?). You didn't include units.When you roll up the wedge to form a cone


the slant height of the cone is the radius of the "round" and the radius of the circular base is half its diameter. I let the height be $h$ inches and then the triangle in the diagram is a right triangle so Pythagoras Theorem gives you

\[h^2 + \left( \frac{38.19719}{2} \right)^2 = 24^2 .\]


\[h = \sqrt{24^2 - \left( \frac{38.19719}{2} \right)^2} = 14.534 \mbox{ inches.}\]


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