volume proportional to scale ratio cubed
1/2*1/2*1/2 = 1/8
so
1024/8 = 128
thank you.
1/2*1/2*1/2 = 1/8
so
1024/8 = 128
We test ships in model basins
say the ship is k times as long as the model
then it is k times as deep
and it is k times as wide
so its volume is k * k * k = k^3 times the volume of the model :)
If you imagine the model to be made up of tiny cubes
then the ship would have to have k times as many rows along the length
and k times as many columns in width
and k times as many high
so it would need k^3 times the original number of tiny cubes to fill it .
Then the height of the small prism is proportional to the height of the large prism
H = k h
and the length is also proportional
L = k l
and the width is proportional
W = k w
so
L W H = k l * k w * k h = k^3 lwh
The ratio of their volumes is the scale ratio cubed.
(by the way the ratio of any equivalent areas on them is the scale ratio squared)
in this case every length on the small one is 1/2 the equivalent length on the big one
so k = 1/2
and k*k*k = k^3 = 1/8
so k = 1/2
Now say we have two cubes
one is 1 cm on every edge
so its volume is 1*1*1 = 1 cm^3
Now another cube (same shape of course)
But it is 2 cm on an edge
so its volume is
2 * 2 * 2 = 8 cm^3
see what happened?
volume = 3 * 3 * 3 = 3^3
Let's say the first cube was 3 cm on an edge
then its volume is
3*3*3 = 27 cm^3
Now say the big one is 6 cm on an edge
its volume is
6 * 6 * 6 = 216 cm^3
BUT I would not do that
I would say
2*3 * 2*3 * 2*3 = 2^3 * 27 = 8 * 27
because my scale ratio is 2
therefore my big volume is 8 times the little one.
so every volume is eight times
here is a sphere with 2 cm radius:
vol = (4/3) pi (2^3)
here is a sphere with 4 cm radius (k = 2)
vol = (4/3) pi (4)^3
2^3 = 8
4^3 = 64
SEE - twice the radius--> EIGHT times the volume
You got it
1024 / 8 = 128 !!
THANK YOU SOOOO MUCH!!!
The smaller volume is 1/8 times the big one