Can one use geometry to measure the volume of something irregularly shaped?
Asked by
Trillian (
21153
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March 19th, 2012
My knowledge of geometry is scanty, at best. As I understand it; Euclidian geometry is used to measure man made shapes like circles, squares, spheres, cylinders, rectangles, etc.
What if I want to measure the total volume of a wrapped piece of mint candy including the wrapper?
Fractals are used to measure shapes found in nature. They were used to more accurately measure England’s coastline and have had countless applications since then.
I don’t actually care about the contest at work, I think the prize is a $50 gift card, it just got to thinking as I walked past it today. There are little green and white striped pieces of candy in a gallon jar. You have to guess the number of pieces. My mind wandered off on a tangent because the pieces are rendered irregular with the wrapping, so that would have to be factored in.
So does Euclidian geometry have a formula for figuring this? Would Fractal geometry be able to more effectively figure this out?
Just curious.
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7 Answers
The most accurate way to measure it would be by the rules of displacement.
As @DrBill mentioned, why not submerge a piece of candy and measure the displacement Archimedes-style?
As I stated, my knowledge of this topic could fit comfortably in a thimble with room for my fingertip left over. I would have no idea how to measure by displacement.
I was more curious to know if there were a practical way to create a formula with geometry that would allow for the wrapper. Since I have no idea how to go about finding that either, I just thought I’d ask.
I defer to your better judgement in this.
If you’d care to be helpful enough to walk me through the actual steps for the displacement thing, that would be a bonus. Maybe you were giving me credit for knowing this already.
Even an accurate measurement of the volume of a single piece won’t allow calculation of the total number of pieces, since you have to take packing efficiency into account. There will be wasted space in between the pieces.
If you can get hold of similar pieces of candy, the empirical approach would be best, where you measure (perhaps by water displacement) the volume of, let’s say, 20 pieces of candy and then extrapolate to the contest jar.
It would be terribly difficult to get any kind of accurate volume for a shape like this via geometry, and then as @gasman said, it would not just be a matter of dividing the total volume of the container by the volume of one piece of candy. There will be a lot of empty space in between the pieces that you’re not taking into account.
Measuring by displacement is simple: fill a graduated cylinder up to a certain level, say, 100 mL. Then drop the piece of candy in so that it is completely submerged in water. The water level will rise by exactly the volume of the added candy. So read the new water level on the side of the cylinder, and from this number subtract the original water level (100 mL), to get the volume of the candy.
The next step I would do is calculate an estimate how much volume is displaced by the packaging. Take a couple of handfuls of candy and measure how high they are in the container. Calculate how much different this would have been from what the water displacement tells you. Use this value in your final estimation of the contest gallon jar.
BTW, the contest was over before I even asked the question. I still haven’t looked to see how many there were, I just got curious to know if there were a way to accurately figure something like this out. I would not have allowed for the space between the pieces.
That second step is a good idea, which I definitely would not have thought of.
Thanks
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