Question

Ginger has 12 plastic bead containers. the containers measure 1 inch on each side. how many rectangular prisms each with a different sized base, could ginger make by stacking all the bead containers?

Answer 1

The volume of each of the plastic bead is determine by multiplying the length, width, and height of the prism which are all equal to 1 in. The volume is therefore equal to 1 in³. The total volume of the 12 plastic beads is 12 in³. To determine the number of rectangular prisms formed, we just have to combine numbers with product of 12. These are,
 Height = 1 in                      12 x 1 x 1 = 12 in³
                                              6 x 2 x 1 = 12 in³
                                                4 x 3 x 1 = 12 in³
Height = 2 in
                                               6 x 1 x 2 = 12 in³
                                               2 x 3 x 2 = 12 in³
height = 3 in
                                              2 x 2 x 3 = 12 in³
Height = 4 in
                                              3 x 1 x 4 = 12 in³
Thus, the answer is 7.