How do you convert between volume measurements?

Its the cube root of the scale used. So if a cube has lengths that are 2cm bigger than another one then the volume would be 2^3 bigger (so 8 times)

If you want to convert between cubic metres and cubic centimetres, for example, you need first to know the conversion fact between metres and centimetres which is 1m = 100cm. The equivalent conversion fact for cubic metres and centimetres will be 1 cubic metre = 100 x 100 x 100 cubic centimetres or in other words 100 cubed. If you are converting say 2.4 cubic metres into centimetres, you would multiply by 1,000,000. If you were converting say 4600 cubic centimetres into metres, you would divide by 1,000,000.

If you are asking about how to work with similar shapes and to be able to identify the scale factor for the volume, then first you find the scale factor of the lengths of two equivalent sides by dividing the bigger length by the smaller length. Then you cubed this length scale factor to find the volume scale factor. Then if you know the volume of the smaller shape and want the volume of the larger shape you would multiply by this volume scale factor. If you know the volume of the larger shape and want to find the volume of the smaller shape then you would divide by the volume scale factor.

Example: Smaller shape A has length of 2, Larger shape B has length of 8

The scale factor of the lengths is 8 divided by 2 = 4.

The scale factor of the volumes will be 4 cubed which is 64.

If you know that the volume of shape A is 20cm3, then the volume of shape B will be 64 x 20 cm3 = 1280cm3.

If you know that the volume of shape B is 640cm3, then the volume of shape A will be 640 divided by 64 = 10cm3.