Question

What do you notice about the surface area and volume for each individual shape versus the surface area and volume for the composite figure?

Answer 1

Suppose that we have two cubes where the side lenghts are L.

The volume of each cube is L^3

The surface of each cube is 6*L^2.

Now, if we add them we have:

Area of both cubes = 2*L^3

Surface of both cubes = 2*6*L^2 = 12*L^2

Now, suppose now that we have a composite shape with the two cubes,

The dimensions of this figure is lenght = L, height = L widht = 2L

Then the volume of the composite shape is L*L*2L = 2L^3

you can see that the volume does not change.

The surface is: 2*(2L*L + 2L*L + L*L) = = 10L^2

So the surface does change: why this happens?

This happens because when we do a composite shape, some surface of both figures is "absorbed" when we put the figures togheter (in this case one face of each cube is being absorved by the composite shape)

So, in conclusion:

Volume is invariant and surface depends on how we do the composite shape.