1. ## Volume of revolution

Hi,
I am new to this forum but I was just wondering If I can get some answers for my maths assignment which I am really struggling with. For my assignment I have to design three water bottles with the volumes of 1L, 600mL and 300mL. The bottles all have to be the same shape with the same proportion. The bottles need to have at least three different functions. I have my 1L bottle designed with all the curves. I used the volume of revolution to determine the 1L volume of the bottle. But, I am having trouble with finding the 600mL and 300mL and their functions being in the same ratio with the 1L. I was just wondering is there any rule that will help me find the volumes and have the same ratio as the 1L bottle i designed.
Any help would be appreciated
Thanks heaps

2. Hello Hels,

It might be a good idea to try and understand why you can't calculate the volume of the 600 ml bottle while you can calculate the volume of the 1L one. Your technique should apply to both cases; if it doesn't then you don't have the right technique.

An $n$ dimensional object, if it is expanded to $r$ times its original size, will have $r^n$ times its original volume. For instance a circle that is twice the radius of another circle will have four times the area; a ball will have eight times the volume of a ball of half its radius.