An Idea for A Culminating Volume/Surface Area Project

As of this week, my geometry classes have begun the final unit of the year - area/perimeter and surface area/volume. I threw out my old unit and am starting anew (let's face it - the old unit was junk). I have some neat hands-on stuff lined up for learning all these concepts. I also am using the apartment project from Sarah at Everybody Is a Genius as my culminating area/perimeter project. I have been considering what to do for the volume/surface area part of the unit as far as the assessment goes. I've done a lot of googling and have found some interesting projects but none that really got at the depth of inquiry and thinking that I want.

So... here's my idea. I'll put the kids in groups of 4. Each group will receive 12-15 nets of 3D figures. I will already have calculated the volume and surface area of each figure. Using combinations of these 3D figures, I will give the groups certain composite 3D figures to assemble with given volumes.

For Example (just making these numbers up):

Group #1 (Each group will have different figures/scenarios):

Combine your figures to make composite 3D shapes with volumes of

(1) 66 cubic in.

(2) 54 cubic in.

(3) 40 cubic in.

(4) 82 cubic in.

Here, I will assess with a rubric for correctness and calculations before students move to part II.

After student groups have successfully grouped their 3D figures, they'll then have instructions on how to assemble them according to surface area calculations.

For instance:
(1) Assemble the figures with a volume of 66 in sq. so that they have a surface area of ________.

(2) Assemble the figures with a volume of 54 in sq. so that they have a surface area of ________.

(3) Assemble the figures with a volume of 40 in sq. so that they have a surface area of ________.

(4) Assemble the figures with a volume of 82 in sq. so that they have a surface area of ________.

The students will tape their figures together appropriately to meet these specifications. I will then grade groups on the correct assembly of their composite 3D figures with a rubric.

Okay, MTBoS.... will this work? What would you change? All input is appreciated.