"Serum...your serum...made me grow...made my brain greater than any human's! Now I want formula...I want to make more serum...to give to insects the world over!! We shall arise...and conquer you puny humans! WE SHALL BE MASTERS OF THE WORLD!" — Krang

Have you read any comic books with unbelievably large creatures?
Have you seen any movies with enormously large people?
Have you ever seen something true to life gigantic?

Although comic books and horror films often prey on fears of the gigantic, many giants do exists.
Be sure to note that "giant" humans are real people with real feelings.
Many "giants" are credited with having larger than life compassion, gentleness, and love for people.

Here are a few rather big fellows.

Andre the Giant weighed in at 500 pounds and stood 7 feet 4 inches tall. " His drive, talent and ambition, however, proved to be as big as Andre himself, and the wrestler became legendary for his achievements in and out of the ring."—Andrethegiant.com
Robert Wadlow grew to a height of 8 feet 11.1 inches. " Robert was the world’s tallest man, but also a kind, thoughtful, spiritual person. He was a successful student, a Boy Scout and even attended college for a year."—AltonMuseum.com
Xi Shun of China towers above his countrymen at 7 feet 8.95 inches. " Xi Shun claims to have been of normal height until he was sixteen when he experienced a growth spurt for unknown reasons, and reached his present height seven years later. He was in the army before returning to Inner Mongolia where he works as a herdsman."—Wikipedia.org

 

Obviously humans are not proportionate to each other. Andre the Giant weighed more than Robert Wadlow even though Robert Wadlow was 1½ feet taller!

What would happen if they were similar?
How much do you think Robert Wadlow would have weighed if he had the same "physique" as Andre the Giant?

Before you answer, think critically for a moment.
Let's first look at a much simpler example to see what happens in 3D figures.

 

Example

A rectangular prism is 4 feet wide, 3 feet deep, and 2 feet tall. What happens to the surface area and volume of the prism if the dimensions are doubled? Quadrupled?
Original	Surface area = 52 ft2 Volume = 24 ft3
Doubled	Surface area = 208 ft2 Volume = 192 ft3
Quadrupled (Doubling the Doubled)	Surface area = 832 ft2 Volume = 1536 ft3

Doubling the dimensions makes the surface area go up by a factor of 208/52 = 4. That's 2².
Doubling the dimensions makes the volume increase by a factor of 192/24 = 8. That's 2³.

Quadrupling the dimensions makes the surface area go up by a factor of 832/52 = 16. That's 4².
Quadrupling the dimensions makes the volume increase by a factor of 1536/24 = 64. That's 4³.

Conclusions:

• Doubling the size of an object does much more than double the area.
• Doubling the size of an object does much, much more than double the volume.

 

Super Important Ideas:

The surface areas of similar 3D figures are proportionate to the square of the ratio of corresponding lengths. The volumes of similar 3D figures are proportionate to the cube of the ratio of corresponding lengths.

 

So to find out how much Robert Wadlow would have weighed if he had the same "physique" as Andre the Giant, the following equation should be used:

Simplifying, we have the equation

Now solving for x:

	Given
	Simplifying
	Rewriting
	Cross multiplying
	Dividing by 0.555

So Robert Wadlow would have weighed about 900 pounds if he'd had the "physique" of Andre the Giant.

Did you catch that? Growing from 7.333 to 8.925 feet changed the weight from 500 to 900 pounds! How could that be?

Remember, to keep a 3D object similar the height, width, and depth all change. That means a change in one dimension affects all three dimensions if that 3D object is to remain similar.

 

So next time you think about doubling the size of a 3D object, remember that the height will double, the width will double, and the depth will double. That will effectively mean the object will be 2·2·2 = 2 ³ = 8 times as big!

Now try your brain out on these problems. Download and practice the problems in Assignment 8.04.