2 rectangular prisms are proportional. the edges of the smaller prism are half as long as the edges of the larger prism. The volume of the larger prism is 1,024 cubic feet. the volume of the smaller prism is what?
thank you.
i know how to get volume,but i need to know how to find the volume of a prism. this prism is proportional to a smaller prism. but the edges of the smaller prism is half as long as the edges of the larger prism. the volume of the larger prism is 1,024 cubic feet. then the volume of the smaller prism is what? i still do not get it. by the way, that's interestinng that you design ships.
if the small prism is proportional to the large prism
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
volume proportional to scale ratio cubed
1/2*1/2*1/2 = 1/8
so
1024/8 = 128
thank you Damon, but how did you get that equation?
Well, you see I am a Naval Architect (ship designer)
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 .
are you still there?
It does not matter the shape as long as the two objects have the same shape.
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)