Section: Math Section 2

33) A wooden cube with volume 64 is sliced in half horizontally. The two halves are then glued together to form a rectangular solid which is not a cube. What is the surface area of this new solid?

1. 64
2. 72
3. 96
4. 112
5. 128

The volume of a cube is equal to an edge cubed, so e³ = 64, and each edge of the cube has length 4. If the cube is sliced horizontally in two, each of the resulting solids will have two sides of length 4 and one of length 2. So when they are glued together, the resulting figure will have one edge of length 2, one of length 4, and one of length 4 + 4 or 8.

The surface area is the sum of the areas of the solid’s six faces. The top and bottom each have area 8 x 4 = 32, the front and back each have area 8 x 2 = 16, and each side has area 4 x 2 = 8. So the surface area of the new solid is
2(32) + 2(16) + 2(8) = 64 + 32 + 16 = 112.