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| Math Central | Quandaries & Queries |
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Question from Peter: I am trying to calculate the diameter of a truncated cone given one diameter the height of the cone and a 10% taper from one end to the other. For example a butter churn is 18" tall and 9" in diameter at the base. the sides need to slope inward at 10% |
Hi Peter,
I drew a diagram with the diameter of the base $D$ inches, the diameter of the top $d$ inches and the height $h$ inches.
Since the taper is 10% the quantity $x$ in the diagram is 105 of $h,$ that is $x = 0.1 \times h.$ Thus
\[d = D - 2h = D - 0.2 \times h.\]
Penny
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