Kellogg just lately launched a brand new line of glazed cereals impressed by glazed donuts. However as an alternative of ring form cereal, they opted for donut holes, which they state, is definitely genius: they are saying there may be extra glaze for a spherical donut gap than a standard donut torus.
I thank Kellogg for utilizing mathematical formulation of their packaging. (Although the torus space formulation must be 4π2Rr
However their declare of the having extra glaze didn’t miss the eye of the web group, which questioned: is that this actually true? Did they do the maths?
Kellogg’s Cereal Has A Math Mistake
Or hold studying.
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“All will probably be nicely in the event you use your thoughts to your choices, and thoughts solely your choices.” Since 2007, I’ve devoted my life to sharing the enjoyment of sport concept and arithmetic. MindYourDecisions now has over 1,000 free articles with no adverts because of group assist! Assist out and get early entry to posts with a pledge on Patreon.
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Kellogg’s Cereal Has A Math Mistake
(Just about all posts are transcribed shortly after I make the movies for them–please let me know if there are any typos/errors and I’ll appropriate them, thanks).
The quick reply is Kellogg’s is mistaken. Here’s a temporary evaluation of the formulation for quantity a torus.
The floor space will be derived equally. We’ve a circle with a fringe of 2πr which travels 2πR, giving a floor space of (2πr)(2πR) = 4π2Rr.
A sphere has a quantity of (4/3)πr3 and a floor space of 4πr2.
We are able to show a particular counter-example. Suppose we now have a sphere of radius 2 versus a torus that has a circle of radius r = 4/(3√π) at a distance of R = 3 from the axis of rotation. The volumes and floor areas are:
sphere
quantity
(4/3)πr3
(4/3)π(2)3
33.51
floor space
4πr2
4π22
50.27
torus
quantity
2π2Rr2
2π2(3)(4/(3√π))2
33.51
floor space
4πRr
4π(2)(4/(3√π))
89.093
The torus has considerably extra floor space for a similar quantity because the dice.
The truth is, the sphere is arguably the worst form. The isoperimetric inequality states a spheres has the LEAST floor space out of all shapes of the identical quantity.
Kellogg, in the event you ever need to use math in your merchandise, I will probably be joyful to evaluation it and share with everybody. As a result of once you say you probably did the maths, you completely DO NOT need to GLAZE over the main points!
References
Nathaniel Olsen, involved engineer and breakfast fanatic
https://www.reddit.com/r/theydidthemath/feedback/1iljmig/self_kelloggs_mathematical_blunder/
https://imgur.com/a/kelloggs-mathematical-blunder-x4o01cz
https://www.reddit.com/r/theydidthemath/feedback/1iljmig/self_kelloggs_mathematical_blunder/
https://www.wkkellogg.com/merchandise/frosted-flakes-glazed-donut-holes
https://www.goal.com/p/-/A-92795149
https://en.wikipedia.org/wiki/Isoperimetric_inequality#In_Euclidean_space
https://en.wikipedia.org/wiki/Floor-area-to-volume_ratio
https://commons.wikimedia.org/wiki/File:Comparison_of_surface_area_vs_volume_of_shapes.svg cmglee, CC BY-SA 3.0
Desmos interactive
https://www.desmos.com/3d/njm9dsdye5
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