3 cubes each of volume 343\text{ cm}^{3} are joined end to end. What is the total surface area of the resulting cuboid?
- A. 343\text{ cm}^{2}
- B. 350\text{ cm}^{2}
- C. 686\text{ cm}^{2} ✓
- D. 700\text{ cm}^{2}
Correct Answer: C. 686\text{ cm}^{2}
Explanation
Side of each cube a = \sqrt{343} = 7\text{ cm}. When 3 cubes are joined end to end, the dimensions of the resulting cuboid are length l = 3 \times 7 = 21\text{ cm}, breadth b = 7\text{ cm}, and height h = 7\text{ cm}. Total Surface Area = 2(lb + bh + hl) = 2(21(7) + 7(7) + 7(21)) = 2(147 + 49 + 147) = 2(343) = 686\text{ cm}^2.
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