Math CentralQuandaries & Queries


Question from Edwin:

In making a 16" dia. cone lamp (stained glass), how many square feet of glass do I need.

Hi Edwin,

I need to know how tall you want the lamp. I need either the height $h$ or the slant height $s.$



We received the reply : h- six &one half” S- 9”

In my digram $ABC$ is a right triangle so Pythagoras Theorem gives

\[S^2 = r^2 + h^2\]

and thus if $r = 8$ inches and $h = 6$ inches than

\[S^2 = 8^2 + 6.5^2 = 106.25\]

and thus $S = 10.3$ inches so I am not sure what value to use for $S.$

Regardless, if you look at Stephen's response to a similar question you will find the expression

\[\frac{\mbox{lateral area}}{\pi \; S^2} = \frac{2 \pi \; r}{2 \pi \; S}\]

which simplifies to

\[\mbox{lateral area} = \pi \; r \times S.\]

I hope this helps,

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