Three identical cubes of edge $4$ cm are joined end-to-end to form a cuboid. Find the total surface area of…

Three identical cubes of edge $4$ cm are joined end-to-end to form a cuboid. Find the total surface area of the resulting cuboid.
  1. $224 \text{ cm}^{2}$
  2. $288 \text{ cm}^{2}$
  3. $192 \text{ cm}^{2}$
  4. $160 \text{ cm}^{2}$

Solution

Resulting cuboid is $12 \times 4 \times 4$. TSA $= 2(12\cdot 4 + 4\cdot 4 + 4\cdot 12) = 2(48+16+48) = 2 \times 112 = 224 \text{ cm}^{2}$.

Asked in: IMO

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