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Math Help - Odd rounded pyramid shape - how to calculate shape/size?

  1. #1
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    Question Odd rounded pyramid shape - how to calculate shape/size?

    I am trying to figure out the "equation" or other means of finding the exact shape in the figure below. It's somewhat of a pyramid with a rectangular base, but the sides are curved rather than flat. I have found how to make the longer sides (simple half-circle) but the narrow two sides I can't quite figure out. The long edge is 40" and the shorter edge is 30".

    Can anyone tell me exactly how to calculate the measurements/curves of the narrower side (third picture)?

    NOTE: The narrow side in the third picture is really just a trial-and-error cut-out, no measurements or calculations were done to determine what it should look like.

    Thanks!





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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by mateoc15 View Post
    I am trying to figure out the "equation" or other means of finding the exact shape in the figure below. It's somewhat of a pyramid with a rectangular base, but the sides are curved rather than flat. I have found how to make the longer sides (simple half-circle) but the narrow two sides I can't quite figure out. The long edge is 40" and the shorter edge is 30".

    Can anyone tell me exactly how to calculate the measurements/curves of the narrower side (third picture)?

    NOTE: The narrow side in the third picture is really just a trial-and-error cut-out, no measurements or calculations were done to determine what it should look like.

    Thanks!


    Can you provide the length (longest side) & width (shorter side) and with a tape measure, give the length along the curved part from the bottom corner to BELOW the rectangle thing on top (just need one assuming all four curved parts are equal). For the rectangle thing on top, just multiply the length x width x height to get the volume for that.





    How tall is this from bottom to top and the length of the bottom edge?
    Can you give me the information I posted under the first picture? Is this for a class or do you just want to figure out the surface area of this? Or did you need the volume of it? You will probably need to use calculus to find the area or volume for this. Get me that info and I'll see what I can do.
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  3. #3
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    This is not for school. I'm building this myself. It's called a softbox, used for photography. There is a light inside and the curved shape helps project the light more naturally than just straight sides.

    The length of the long side (from the semi-circle-ish shape) is 40". The shorter one (the one I need to find the shape of) is 30". I'm not bad with calculus but just need a start on what exactly to look for. The box on top contains the light and is 6.5"x6.5"x1.125". Not sure that the height really matters and not sure why volume matters either. Can you explain why you asked for that part?
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    I created this with Google SketchUp (a great tool for geometry, by the way), and it's not right. I tried to cut the thing out of same sheet of material, but that's not necessary for the project. Duct tape will work just fine... if it can't be fixed with duct tape and bubble gum it's just BROKEN, right? The top and bottom shapes are exactly the way they should be. The left and right I just created by extending the radius of the top and bottom shapes and drawing a line to connect them. But again, this one is NOT right.

    If you would like the SketchUp file I can provide that too.

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  5. #5
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by mateoc15 View Post
    This is not for school. I'm building this myself. It's called a softbox, used for photography. There is a light inside and the curved shape helps project the light more naturally than just straight sides.

    The length of the long side (from the semi-circle-ish shape) is 40". The shorter one (the one I need to find the shape of) is 30". I'm not bad with calculus but just need a start on what exactly to look for. The box on top contains the light and is 6.5"x6.5"x1.125". Not sure that the height really matters and not sure why volume matters either. Can you explain why you asked for that part?
    I guess I'm not sure what you are trying to find out. Your post says "how to calculate shape/size" so are you wanting to figure out the volume of the object, its thickness? Or are you looking for the surface area? Because this is an irregular shape, you could take the height of the curved part and make a function based on that and the width of the bottom and then calculate the area or the volume using an integral to calculate the area using the height as your limits. Just an idea. I guess I'm just not sure what exactly you are trying to determine. Let me know if I can help.
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  6. #6
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    Let me define the question a little tighter...

    I am 100% sure of the exact shape I need for the semi-circle sides. It's a semi-circle with a diameter of 40". What I want to do is find out how to cut the narrow end out of a sheet of material. Obviously the top will be 6.5" long (to match up to the box at the top) and 30" across the bottom. But there has to be some method to determine the curves on that narrow piece.

    The shape is what I'm looking for. I'm not interested in any volume or area.
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