This is a problem I'm trying to solve while creating a simple app by importing a 3D model (of any shape) and applying some changes to it, namely, increasing the size of the model.
When a model is imported, its volume and dimensions are automatically calculated by the 3D model library.
I calculate the dimension increase or decrease in percentages manually e.g. model increase:
$perc = \frac{increase - initial}{initial} \times100$
If the model's dimension is at default 100% and the volume is say $1800cm^3$ what will the volume be if the dimension is increase by say 15% ?
I don't know how to determine a formula for this. Can anyone help me please?
If each length is to increase by a 15% then it is to increase by a factor of 1.15. now if you have a unit cube for example the cube will be of volume $ 1.15^3 $ because the formula for a cube is $ l^3 $ where l is the length of a side and if they all increase by a factor 1.15 we have the new length of a side of the cube is 1.15l and thus the volume is $ (1.15l)^3 $ We can apply the same concept to other shapes based on which lengths you are increasing.
This is called the volume scale factor of enlargement for 3D shapes and would be the Area scale factor for 2D shapes. So if you are still confused searching up them terms will help.