# How to calculate volume change with size change?

If I know the volume of a kayak is 86 gallons, is there a way to calculate what the volume would be if the kayak was 1” deeper along the full length of the kayak?

It would certainly be possible (within a certain margin of error) to calculate this if you had the dimensions of the kayak–but I’ll guess that you don’t. If you had a few pictures of the kayak, then you could perhaps guess at its proportions and come up with approximate dimensions. With only a volume, however, there is no way to say what would happen by increasing one dimension.

If the two kayaks were in the same proporations, then you could calculate it, assuming you knew all the dimensions. (The same proporations would require the deeper kayak to be longer and wider.)

To get a ballpark figure, fill your exiting vessel to the one inche level. Just eyeball it and then measure the water. Should be close enough for government work.

The extra inch is added at the center seam. By that I mean where the bottom hull part and top deck part are joined. So if you measured the depths along the length of the kayak the depth would be one inch deeper at every point. The width and length would remain the same.

And I do know the basic dimensions, that being maximum length, width and depth, but kayaks are pretty convaluted (sp?) so I don’t know if those dimension would help.

If you make some basic assumptions as to how each dimension is changing, you could try to model it as a related rate problem. But, it’s been awhile so I throw this out as a suggestion maybe some other SDoper can take off from…

• Jinx

Well, you can certainly say that the volume change is less than (maximum width) x (maximum length) x (1 inch). If your kayak is anything like all the kayaks I’ve ever seen, I would guess that the actual volume change is somewhere between half and two-thirds that figure.

Thanks everyone. Looks like the only way to do it is fill the thing with water. Blah!

We need rather more information than you’ve given. In general, the volume of an object is in proportion to the cube of a dimension.