Maths question about building a funnel
May 7, 2015 11:33 AM   Subscribe

I'm trying to work out the measurements to cut 4 pieces of metal and it's completely wrecking my head.

I'm making a funnel with 4 flat sides. Think of it as a pyramid with the top cut off. The base is square with sides of 250 mm. The height (after top is cut off) is 250 mm. The narrow end of the funnel is also square with sides of 70 mm. I found an on-line calculator that will calculate pyramid measurements if you enter the base and height but I don't know the height. I only know the height should be 250 mm after the top is cut off. I need to know what height to cut the 4 pieces of metal. It would also be nice to know the angles on each piece. Thanks.
posted by night_train to Science & Nature (9 answers total) 1 user marked this as a favorite
Best answer: 70mm is 28% of 250mm, so you will be cutting off 28% of the pyramid's height (since the side length varies linearly with the height). That means the height before cutting off the top is 250mm / (100% - 28%) ≅ 347.2mm.
posted by mbrubeck at 11:38 AM on May 7, 2015

Best answer: Instead of thinking it as a pyramid with its top cut off, think of it as a 250mm-tall pyramid with each side sheet cut in half vertically and a 70mm wide strip inserted. Bad ascii depiction: /\ -> /| |\
posted by supercres at 11:42 AM on May 7, 2015 [1 favorite]

Best answer: Before you assemble, you will have 4 pieces of metal, each the same, symmetric, trapezoidal shape...

They will be 70mm wide at their skinny side, 250mm wide at their fat side, and 265.7mm long. If you lay out the pieces and draw those dimensions on them, you can connect the dots with straight lines and you won't need the angles. If you do need them, trig can get you there.
posted by milqman at 11:43 AM on May 7, 2015

Best answer: Use your online calculator as if for a pyramid with a square base 250mm - 70mm = 180mm. That will give you the measurements for triangular sides. The height and the side length for those triangles will be the same as those for the trapezium sides you actually need for your funnel.

In other words, instead of thinking about converting triangles to trapezia by cutting off the tops, just keep them the height they are and smear them sideways.
posted by flabdablet at 11:45 AM on May 7, 2015 [1 favorite]

Cut four sides of the funnel, as the lower part of the pyramid side. Think of the shape as a rectangle that flares into a parallelogram at the top. Leave enough extra on each side of the one quarter funnel, to fold and rivet into the funnel shape you are making. Are you soldering, welding, glueing or riveting the form together? You will have to make a small cut where the rectangle joins the pyramid, on the left side of the rectangle top just as wide as the fold to accommodate folding.

\ /
|| this is vaguely one of four, without the gap between the upper and lower.
posted by Oyéah at 12:00 PM on May 7, 2015

The method suggested by supercres and flabdablet method is ingenious and will give you a funnel that with base side 250mm, height 250mm, and top side 70mm, as requested.

However, it won't be the exact same shape as a 250mm-high pyramid with its top chopped off. The angle will be slightly different. If you extend this funnel's sides to form a complete pyramid, it would be about 277mm high.
posted by mbrubeck at 12:10 PM on May 7, 2015

Sorry, my last comment was incorrect; I forgot that the desired height is 250mm after the top is chopped off, not before. supercres and flabdablet are correct, and their method should give you the same result as my original answer.
posted by mbrubeck at 12:12 PM on May 7, 2015

Response by poster: Many thanks to you all for taking the trouble to answer. The method suggested by supercres and flabdablet is indeed ingenious. It would have taken me a long time to work this out on my own.
posted by night_train at 12:32 PM on May 7, 2015

Response by poster: As can be seen the results were perfect.
posted by night_train at 5:20 AM on May 8, 2015 [1 favorite]

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