The power of the dimension determines the size of the change in the volume value:
If a dimension in the volume formula is raised to a first power, the volume changes by the same factor as the shape.
For example: A rectangular pyramid volume formula is V=1/3 lwh. The length, width and height in the formula are raised to a first power. If we double the length or the width or the height (one of them), then the volume will also be doubled.
If a dimension in the volume formula is raised to a second power, when the shape changes by a factor the volume changes by a square of the factor.
For example: A right circular cone volume formula is V= 1/3 πr2h. The radius of the circle is raised to a second power. If we double the radius, the volume will change by 22=4. The height in the formula is raised to a first power. If we double the height, then the volume will also be doubled.
If a dimension in the volume formula is raised to a third power, when the shape changes by a factor the volume changes by a third degree of the factor.
For example: A sphere volume formula is 4/3 πr3. The radius of the sphere is raised to a third power. If we double the radius, the volume will change by 23=8.