Question

If the areas of three adjacent faces of a cuboid are 6 cm², 8 cm² and 27 cm², then its volume is ________.

Answer 1

Let the length, breadth and height of the cuboid be l cm, b cm and h cm, respectively.

Therefore, the areas of the adjacent faces of the cuboid are lb, bh and hl, respectively.

Now,

lb = 6 cm² .....(1)

bh = 8 cm² .....(2)

hl = 27 cm² .....(3)

Multiplying (1), (2) and (3), we get

lb × bh × hl = 6 cm² × 8 cm² × 27 cm²

⇒ l²b²h² = 1296 cm⁶

⇒ (lbh)² = (36 cm³)²

⇒ lbh = 36 cm³

Thus, the volume of the cuboid is 36 cm³.

If the areas of three adjacent faces of a cuboid are 6 cm², 8 cm² and 27 cm², then its volume is ___36 cm³___.