Math CentralQuandaries & Queries


Question from Sash, a teacher:

Dear teacher,
how do i form a paper cone with the height of 25 cm, the slant height of 25.8 cm, and the radius of 6.2 cm?

Please's a huge emergency!


Hi Sash.

Take a look at this explanation from Penny which tells you how to make patterns for cones.

In your case, you will need to cut a sector of a circle (like the bottom diagram on that page), where the radius equals your slant height and the angle at the point is 86.5 degrees.

Here's how I calculated that:

Angle = 360 x (circumference of cone base / circumference of circle)
= 360 x (radius of cone base x 2 x pi) / (radius of circle x 2 x pi)
= 360 x (radius of cone base / radius of circle)
= 360 x (radius of cone base / slant height of cone)
= 360 x 6.2 / 25.8
= 86.5 degrees.

Stephen La Rocque.>

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