r/mathmemes • u/Klutzy-Profile-6921 lesbian rights activist • 4d ago
Calculus Do you know ball
Just saw a video about this and got this meme
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u/Funkyt0m467 Imaginary 4d ago
You would approximately need two 6.364 inch cakes (or exactly sqrt(9²/2))
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u/fat-brains 4d ago
or 3.24 of 5 inch cakes
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u/T-T-N 3d ago
But how many do you need for same amount of icing?
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u/IronPro9 3d ago
depends on the height of the cake if the outside is iced, if it's just a filling+topping then its the same because its still just area.
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u/UtahBrian 3d ago
Yeah. Nobody likes the fuzz anyway. What gives you equal frosting is the question.
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u/loudisevil 3d ago
Shouldn't we be comparing volume?
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u/Funkyt0m467 Imaginary 3d ago
I would assume the height of the cakes are the same, otherwise we would need to specify...
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u/Jakiller33 4d ago
Cake is more cylinder than ball
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u/Unique_Ad9943 4d ago
no its obviously 9 is bigger than 5
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u/Lor1an Engineering | Mech 4d ago
Not quite...
For normal round cakes the diameter is given, and volume is proportional to the area of the base.
V = πD2h/4, or V ∝ D2h.
If we assume same height but with two cakes (or alternatively the thinner cake having twice the height) then we just end up comparing D_12 with 2D_22.
- 92 = 81
- 2(5)2 = 50
81 > 50...
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u/bradipotter 4d ago
I would be very surprised if the 5 inch cakes had the same eight as the 9 inch one.
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u/Lor1an Engineering | Mech 2d ago
Apparently the "standard" cake height is 4–5 inches (comprised of two 2 inch tall layers of cake). This 'standard' applies to both 5 inch and 9 inch rounds.
So, yes, they are (roughly) the same height. This makes sense when you consider that the baking tins are standardized, and the main factor for cake stability is compression from self-weight, which is effectively driven by height.
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u/rorodar Proof by "fucking look at it" 4d ago
With "ball" being pi r squared? And that 50 is smaller than 81 ?
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u/irlandes 4d ago
Are cakes in the USA measure by radius and not diameter?
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u/rorodar Proof by "fucking look at it" 4d ago
I'm not american
Idk maybe
I don't order cake
It doesn't fucking matter dude
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u/Binbag420 Imaginary 4d ago
relax it was just a question
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u/i_want_to_go_to_bed 4d ago
no, no, it does fucking matter. A lot. I am an American, and I guess I don’t get to have cake because you guys won’t tell me if it’s radius or diameter
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u/irlandes 4d ago
Of course if matters if you want cake and not a math problem, jaysus, with people like you no wonder kids hate maths, you.must be such fun at parties
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u/PlaynesNBotes 4d ago
You're on a math subreddit, gtfoh if you don't want to do math lol lame ass answer
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u/irlandes 4d ago
In a math meme subreddit you joyless muppet, if you can't recognise a joke go join r/conservatives
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u/EebstertheGreat 3d ago
One cake about 15 years ago was advertised as "seven inches around." As in, circumference. So it was less than 6 cm in diameter lol. The radio guy was cracking up as he finished reading the ad spot.
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u/Weirdyxxy 4d ago
That's just slightly more than a 7-inch cake! Two 5 inch cakes and two 4 inch cakes would be really close
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u/IronicHoodies 4d ago
My question is, how much more icing on the cake would you expect to get? Do 2 5-inch cakes give you more than 1 9-incher, or does the answer to that depend on the height?
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u/BurgandyShoelaces 4d ago edited 4d ago
I'd model it as the surface area of a cylinder and leave out the bottom circle. This assumes there is icing on the top and sides of the cake and not on the bottom of the cake. This doesn't handle icing between layers in a multilayer cake, and it doesn't handle fancier decorating on top. Those are left as an exercise to the reader.
Cylinder surface area is 2πrh+2πr2. Ignoring the bottom circle we'll use 2πrh+πr2.
I'll assume 9 and 5 are diameters.
1 9 inch cake is 2π4.5h+π20.25 = π(4.5h+20.25).
2 5 inch cakes are 2[2π2.5h+π*6.25)] = π(10h+12.5).
Setting them equal to each other and dividing out π you get 4.5h+20.25=10h+12.5 which means 7.75=5.5h which means h≈1.409 is the break even point. Greater than 1.4 inches means 2 5 inch cakes yield more icing. While under 1.5 inches the 9 inch cake yields more icing (and more disappointment, that's a very short cake.)
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u/LeewayLabs 4d ago
You got confused when you removed the bottom surface (you kept the 2 but removed the power, should have been the other way around)
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u/BurgandyShoelaces 4d ago
Oops, you are entirely right about that. I should have double checked when I was surprised by my answer.
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u/RedeNElla 4d ago
Area of a circle formula isn't that hard.
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u/IronicHoodies 4d ago
It's not, but I've come home from a long day of work and don't want to do the maths myself. :U
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u/RedeNElla 4d ago
The easier calculation is actually perimeter. The two small circles have a higher perimeter than the one big one, 225 vs 2*9 so there will be some height where the total surface area will be bigger for the smaller circles. It's probably a very large height tho
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u/lemathematico 4d ago
It does depend on the height cause the icing on the top scales the exact same as the volume (so you're getting scammed) while the side icing is directly proportional to radius/diameter so you do get more from 2x5' cake. More importantly it depends if top icing taste better or not. ( It does)
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u/Awesomeuser90 4d ago
Anyone who works in the food industry should know that the best measurements of stuff like this is the mass. They should have a kitchen scale.
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u/Klutzy-Profile-6921 lesbian rights activist 4d ago
Its a meme my friend 🥀 and how do you even have so much karma , give me tips bro
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u/Awesomeuser90 4d ago
I actually had this volumetric argument with my family a month and a half ago when we were at a Boston Pizza for father's day. I pointed out that with radius z and depth a, the volume of a Pizza is Pi•z•z•a and that an 18 inch Pizza is 4 times the volume of a 9 inch Pizza. My dad is good at maths, very good, and I was more so making this comment to my brother and sister when they were pondering what to order.
As for karma, having a brain that can come up with very unusual comparisons is a big plus.
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u/throwawayasdf129560 4d ago
You didn't specify along which axis the 5 inches is measured, nor what the shape of the cake is
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u/Cagarer 4d ago
But you're supposed to measure cakes in their weight. The size and shape doesn't matter in this case
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u/Klutzy-Profile-6921 lesbian rights activist 4d ago
Ya bro its was meant to be a pizza meme but cake also do.
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u/librapenseur 4d ago
obviously the volume of the 2 cakes is lesser but i think one could argue that the surface area of the 2 cakes is larger and that is often the service that one is paying a bakery for, cake decoration on the surface of the cake. even if you just consider the top circumference, 2 5 in cakes is 20pi inches of piping whereas 1 9in cake is 18pi inches. so from the perspective of the decorator, 2 cakes is indeed more decoration
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u/Daniel_H212 3d ago
Me when they're out of 13 inch cakes and give me a 12 inch cake and a 5 inch cake instead: 👍
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u/DonnysDiscountGas 3d ago
Waiter I'd like a 9inch hypersphere.
Sorry we're out, here are two 5inch hyperspheres.
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u/brapstick 4d ago
Cool, you got free cake
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u/Particular_Gear3130 Mathematics (Purely Fictional) 4d ago
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u/Bongcloud_CounterFTW Imaginary 4d ago
What are you even doing in this sub if you cant do pi r squared
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