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 cubic units, where k is a natural number. What is the total surface area of the cuboid?

Question

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 cubic units, where k is a natural number. What is the total surface area of the cuboid?

Accepted Answer

62 square units. xyz = 30k³ with x, y, z all prime and x > y > z. 30 = 2 × 3 × 5. Since x, y, z are primes with z < y < x, and product equals 30k³, the natural choice is x = 5, y = 3, z = 2 (giving k = 1). Total surface area = 2(xy + yz + zx) = 2(15 + 6 + 10) = 2(31) = 62 square units.

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 cubic units, where k is a natural number. What is the total surface area of the cuboid?

Explanation

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