# There is a rectangular prism made of 1 in cubes that has been covered in tin foil.

There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure e in inches of the width of the foil covered prism?

## Answer/Solution

10

### Steps/Work

If the width is w, then length and height would be w/2.

So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)

=> w = 2*4 = 8 in.

Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes

= 8 +2=e =10

Ans E.

So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)

=> w = 2*4 = 8 in.

Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes

= 8 +2=e =10

Ans E.