# math

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A box has a volume of 48 cubic cm. A similiar box has volume of 6 cubic cm. what is the scale factor between each box?

• math -

(48/6)^(1/3)
= 8^(1/3)
= 2

for example if a little cubical box had length 1 and a big one had length 2
then the volume of the little one is 1^3 = 1
and the volume of the big one is 2^3 = 8

so a scale ratio of 2 leads to a volume ratio of 8

• math -

By the way, you happened to ask a ship designer.

• math -

thank you!

• math -

You are very welcome. I am used to model ships and the real things.

• math -

can prime other than 2and 5 3 apqrt
explain

• math -

n and n+3
If n is even (not prime), n+3 is odd
If N is odd, n+3 is even (not prime)
2 is the only even prime number, all bigger ones are divisible by 2.

• math -

damon i need to now where you got 1/3 from

• math -

(Vbig/Vsmall)^(1/3) is the cube root of the volume ratio

the volume is proportional to the scale ratio cubed.

If you have a scientific calculator
try
8^(1/3)
and see if you get 2

Most of us know by heart that 2^3 = 8 and 3^3 = 27 and 5^5 = 125

• math -

The 1/3 power comes from if A is the scale ratio
then to get volume the x dimensions and the y dimensions and the z dimensions are all multiplied by A
So the volume of the big one is A^3 times the volume of the little one.

• math -

thank you i get it now your awesome

• math -

You are very welcome.

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