# Small is Mighty: the Square-Cube Law

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What do you think is stronger,

an ant or an elephant? An elephant can lift

more weight than an ant, but what about their strength

compared to their body size? The answer might surprise you. An elephant can lift

500 kilograms, which is 10% of its body weight. An ant can only live

one-millionth as much, but that amount is actually

50 times its body weight. Ants use their

impressive strength to move food and materials

to their colonies. How much can you lift? The average person between the

size of an ant and an elephant can only lift about

half of its own weight. Why is an ant so strong? First, we need to understand

a principle called the square cube law,

which Galileo came up with over 400 years ago. He observed that when

an object grows in size, its volume increases

faster than its area. Let’s picture a cube. The area of one face on the

cube is a length squared, and the volume is a

length cubed, hence, the square cube law. This cube has sides that

are 1 centimeter long. The area of a face on the

cube is 1 squared centimeter, and its volume is

1 cubic centimeter. Now this cube has sides

that are twice as long. The area of its face is

4 squared centimeters, but the volume is now

8 cubic centimeters. Doubling the length of the

sides quadruples the area, but octuples the volume. As the object gets bigger,

the ratio between its area and volume changes. They’re important consequences

when an objects volume grows faster than its area,

because it changes the way, it could interact

with its surroundings. The effects of the

square cube law can be observed in

our everyday life, for example, in

designing buildings. We can make small scale

models of buildings out of paper mache,

but real houses are made of wood

brick and metal. But why can’t we just build a

real house out of paper mache? The amount of weight that

a structure can support is relative to the

cross-sectional area, but the buildings own weight

is proportional to volume. Since the square cube law told

us that volume increases faster than area, a bigger

building will weigh more, but might not have enough area

to support its own weight. These two towers are made

of the same materials, but only the small one can

support its own weight. Because of this engineers

need to use stronger materials like bricks to design

real buildings that have larger dimensions. For a similar reason,

an ant can carry more, relative to its body

weight, than an elephant. And this is also the reason

why monster ants do not exist. Strength is proportional

to a cross-sectional area of their legs, while weight is

proportional to their value. Here you see a small

ant holding its weight. If we now scale

up the ant, we see that the ant’s legs can no

longer support its weight, and it collapses. And hey look, the small

ant can even bring treats back to its friends. The square cube law

is also observed in aerodynamics, which is the

science of flying and falling. You may have learned that

gravity causes matter to fall towards the

ground, and that gravity makes objects of any mass

fall at the same speed. Why is it then,

that in real life, some objects seem to

fall faster than others? A falling object actually

experiences two forces, gravity and air resistance,

which is also called drag. Gravity makes the

objects falls faster, while drag slows it down. The force from gravity is

proportional to the volume of an object, while drag is

proportional to its exposed area. Remember again that

when things get bigger, volume increases

faster than area. If we drop these two different

size helicopters from four stories high, what happens? As predicted, the

bigger helicopter fell faster, because the

drag, which goes with area, increases more slowly than

weight, which goes with volume. Let’s review what

we’ve learned today. The square cube law

tells us that when an object grows in size,

its volume increases faster than its area. We’ve seen how this can

be applied to buildings, animals, and falling objects. Look around you,

what else can you explain with the

square cube law?

Sophia MPost authorFirst Comment YAY!!!! 😀

MoongazerrPost authorCongrats 🙂

rasecsexiPost authorI learn something today. It was Awesome! d=(^.^)z

Chiranjeev ThomasPost authorstrength–directly proportional– to cross section area of the legs??? ……. doesn't an opposing force like the muscles or the MATERIAL used to support the structure matter?? i mean.. one can balance an insane amount of weight on 4 diamonds standing as pillars but covering a small surface area

Captain ApolloPost author2:46?

Sophia MPost authorThx

DerkasaurusPost author"average human can only lift half his own weight" looks like somebody has never been to the gym.

Melanie Hevel-OlsonPost author@NevolmonGaming *SMH*… I hope you were kidding with that ignorant comment and that you do actually understand the meaning of "average" when trying to generalize to billions of people. If you weren't kidding, I'd be willing to explain it to you 😛 I'm concerned you weren't kidding simply because I cannot imagine making such an inane statement in response to a video like this.

haseothepkkerPost authorI WANT THOSE STAR BURSTS!!

I WANT THEM THEY'RE MINE!!

Ichigo BleachPost authorIts only my humble opinion.

All of this is only HALF TRUE. Gravity play a MAJOR ROLE. Unless u ENLARGE an ANT, maybe ANT also cant SUPPORT more weight because of GRAVITY.

Also CUBE LAW sometimes doesnt apply to ALL. There is sometimes LARGER object with LARGER volume but with SMALLER MASS. I mean THE CUBE is LIGHT. Compare to SMALLER CUBE.

Angel AlvarezPost authorI have a friend in high school who is only 163 pounds and can lift almost 400 pounds.

Adam HowlettPost author"Gravity makes objects at any mass fall with the same speed"

Oh dear.

carultchPost authorAn elephant is 100 times larger than a mouse per linear size, and weighs 500000 times as much. Lighter than equal densities/equal proportions would predict, but it is still the right order of magnitude.

A mouse's femur is 1.1 cm long, with a diameter of 0.7 mm.

An elephant's femur is 1 meter long.

If direct compression pressure were the governing failure mode, we'd expect an elephant's femur to have a diameter of 50 cm. A square-cube law, exactly as this video would predict. This is an extremely impractical femur, to be so thick that its thickness is half its length.

If buckling were the governing failure mode, we'd expect an elephant's femur to have a diameter of 18 cm. This seems much more reasonable, but it still is seems rather thick for a bone proportion.

The actual femur of an elephant is 8.6 cm in diameter. The ratio of diameter to length is only slightly larger for the elephant (0.086) than for a mouse (0.063). Not nearly enough to justify either scaling argument.

Something else is going on here. Anyone know what it could be?

M DPost authorThe elephant

Abdallah Ezzat - KojiPost authorthe square cube law should work all the time right.

but it confuses me when we deal with fractions.

lets say we have a cube, its volume is L^3, and its cross section is L^2.

So if we start with L=0.1("unit"), then its cross section is 0.01 (unit squared), and the volume is 0.001 (unit cubed).

When the dimension doubles to become 0.2 (unit), the cross section grows four times which is 0.04(unit squared), and the volume grows eight times faster which is 0.008 (unit cubed).

Hummmm…..

I knew what what seemed wrong, I mistook that the values before 1 (unit) is greater for lower powers. However, still the higher powers always have a higher rate of increasing (which is the idea), and the values pass the breaking point at 1 (unit).

It creates an illusion jumping between different units of measure. take a 2 cm, the cross section is 4 cm^2, and the volume is 8 cm^3, it is not right to compare different types of quantities e.g. a volume and a cross section. still numerically 8 is greater than 4, "the volume is greater than the cross section". If we take the same cube and measure it in meters, its length is 0.02 m, cross section 0.0004 m^2, and the volume 0.000008 m^3. numerically 0.000008 is smaller that 0.0004, "the volume is smaller than the cross section".

Anyways it is one of the times when you know the answer to your question right after you speak out you question.

Johan WestinPost author1:05

[Gallileo Intensifies]KeppaKopPost author0:48 do you even lift bro?

Marco PoloPost authorThis. Is a pile of shit atoms. are round not square so this theory. Is garbage just look at the ant. Its body part are round not square infact a small square. I could smash easy with a hammer. If. Its steel but a large steel square would take me hour's to smash. what century are you living. In. If. It was a small steel ball. It would be harder for me even. If. It was bigger. It would still be hard to smash

Marco PoloPost authorand. If square's are weaker when there bigger why are building square why. In the hell would anyone make a square house or building period this shit. Is stupid

Marco PoloPost authorand the ant. Is able to pick more weight because gravity dont effect smaller objects. that's why the ant has a shell around. It's body because gravity has almost no effect on. It so. It has pure muscle beneath the shell

Richard StrawnPost authorgod your voices are so fucking annoying.

blessvicPost authorwhat are the example of economic of scale due to cube square rule

Rulersonic BoomPost authorHmm Good explanation here's a sub for ya.

Clicks the subscribe buttonNate BakerPost authorWhere is the actual equation?

TheKKKandTerroristPost authorelephants can lift 9000-10000kg wtf 300-500kg is just their trunk alone….

GoatPost authorHALF OF MY WEIGHT?! Bitch I weigh 130 and squat 160. What you talking about 'half of his own weight'

Weak ass plebs

Aaron DrayPost authorThis is why honey I shrunk the kids could not happen.

Reese ArcherPost authorso if you have a bunch of ants working together to make one big ant-elephant, would the ant-elephant be stronger than the elephant?

ToxicSkull0Post author2:16– Rain

dazhibernianPost authorThe ants are on roids.

Sealson KataruPost authorThis is a great video

Slxy-FaultyPost authorim 14 and I weigh 75 kg and lift 80

superzilla784Post authorFunny thing is that the Square Cube Law was actually mentioned in the 2016 movie. when Godzilla first arrived at Japan, the senator called a meeting to calm everyone down. "The creature cannot come up onto land without crushing itself under its own weight" but then Godzilla gave a middle finger to science and came up onto land anyway. Lol

Sheev PalpatinePost authorSo most people cannot do pullups?

Mac manPost author..In this video: https://www.youtube.com/watch?v=WQGw1tKEpEg

The Antichrist Irrefutably Identified! • The “Beast” …666

Dr Ankit Panigrahi IndiaPost authorYou ignored a crucial parameter and that's density .

Tomas DrakePost authorLOBO

Adrian ArshadPost authorAccording to the science present here, I'm not actually that fat.

Hacher UnfriendedPost authorAn ant can lift 50x its weight but if it's weight is twice bigger, it topples. What's logic in that?

Kevin MarioPost authorWho else came here from Yahtzee's RE2 review?

Menace VangPost authorDamn Galileo be making everyone look like a slacker

Milk and Cookies ProductionsPost authorWho else watched cuz they though it was a dick joke?

Kieran mPost authorNot even gonna lie, just thought of attack on titan the whole time

Shammo HamidPost authorI love physics.

tommy d u b b sPost authorThis is like how something is faster the smaller it is….but this is about strength

Seth GizenPost authorWell time to shrink myself to the size of a quark.