Let x, y, z (all prime) be the length, breadth and height respectively of a cuboid with x > y > z. The volume of the cuboid is 30k^3 cubic units, where k is a natural number. What is the total surface area of the cuboid ?
- A. 60 square units
- B. 62 square units ✓
- C. 64 square units
- D. Cannot be determined due to insufficient data
Correct Answer: B. 62 square units
Explanation
Volume V = xyz = 30k^3. Since x, y, z are primes, the product xyz can only have 3 prime factors. 30 = 2 \times 3 \times 5 (which are 3 primes). Thus k must be 1. The dimensions are x = 5, y = 3, z = 2. Total surface area is 2(xy + yz + zx) = 2(15 + 6 + 10) = 2(31) = 62 square units.
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