Math CentralQuandaries & Queries


Question from anonymous, a student:

A cone is inscribed in a hemisphere. the slant height of the cone is 20cm. When cut along its slant height, the cone forms a sector of a circle.
find the angle of the sector, to the nearest 1 decimal place.


In my diagram


$CA$ and $BC$ are both radii of the hemisphere and hence are of the same length, call it $R$ cm. Triangle $ABC$ is an isosceles right triangle with hypotenuse of length 20 cm so Pythagoras Theorem will help you find the value of $R.$ Now use the procedure in Harley's response to an earlier question to complete the solution.


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