Answer:
A. 162
B. 128
Step-by-step explanation:
We have wooden cubes of 2 in of side.
A. If the box is 18 x 12 x 6 in., in the base (18 x 12), we can fit 54 cubes:
![\dfrac{18}{2}\cdot \dfrac{12}{2}=9\cdot 6=54](https://tex.z-dn.net/?f=%5Cdfrac%7B18%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B12%7D%7B2%7D%3D9%5Ccdot%206%3D54)
As the height is 6 in, we can fit 6/2=3 layers of 54 cubes in the box, se we can fit 162 cubes:
![B=3\cdot54=162](https://tex.z-dn.net/?f=B%3D3%5Ccdot54%3D162)
B. If we have a box with measures 16 x 9 x 9 in., and the base is 16x9 in, we can fit (16/2)*(9/2)=8*4=32 cubes per layer.
Note that in the 9 in side we can only put 4, as we need 10 in to fit 5 cubes (we can not cut them).
In the same way, as we have 9 in of height, we can fit 4 layers of 32 cubes, so this is a total of 128 cubes:
![B=4\cdot32=128](https://tex.z-dn.net/?f=B%3D4%5Ccdot32%3D128)