2026 · Q70
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 30k³ units, where k is a natural number. What is the total surface area of the cuboid?
Elementary MathematicsNumber System
- A60 square units
- B62 square units
- C64 square units
- DCannot be determined due to insufficient data
Explanation
Since x,y,z are primes with xyz=30k³, we must have k=1 and {x,y,z}={5,3,2}. The total surface area is 2(5·3+3×2+2·5)=2(15+6+10)=62 square units, option B. The 'cannot be determined' option ignores that a product of three primes fixes k=1.