Question

There are 4 identical wooden blocks that are 20 inches long, 2 inches

wide and 1 inch thick. If you glue them together, what is the difference
of the largest and smallest outer surface area you can get?

Answer 1

Explanation:

Each block has two 20×1 faces, two 20×2 faces, and two 2×1 faces.

Surface area of one block = 2(20×1) + 2(20×2) + 2(2×1) = 124 sq in

Total surface area = 4(124) = 496 sq in.

Largest surface area: Assemble the blocks end-to-end into a block that is 80 by 2 by 1. Six of the 2 by 1 faces are hidden, so the surface area is 496 - 6(2×1) = 484 sq in.

Smallest surface area: Assemble the blocks into a block that is 20 by 4 by 2. Four of the 20 by 2 faces and four of the 20 by 1 faces are hidden, so the surface area is 496 - 4(20×2) - 4(20×1) = 256 sq in.

Difference in surface area = 484-256 = 228 sq in.