Question

If the sides of a cubic box are increased by 1, 2, 3 units respectively to form a cuboid, then the volume is increased by 52 cubic units. Find the volume of the cuboid

Answer 1

Let the side of the cube be ‘x’

Sides of cuboid are (x + 1)(x + 2)(x + 3)

∴ Volume of cuboid = x³ + 52

⇒ (x + 1)(x + 2)(x + 3) = x³ + 52

⇒ (x² + 3x + 2)(x + 3) = x³ + 52

⇒ x³ + 3x² + 3x² + 9x + 2x + 6 – x³ – 52 = 0

⇒ 6x² + 11x – 46 = 0  ......(÷2)

⇒ (x – 2)(6x + 23) = 0

⇒ x – 2 = 0 or 6x + 23 = 0

⇒ x = 2 or x = `- 23/6`  ......(not possible)

∴ x = 2

Volume of cube = 2³ = 8

Volume of cuboid = 52 + 8 = 60 cubic units