If the areas of three adjacent faces of a rectangular box

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If the areas of three adjacent faces of a rectangular box which meet in a corner are 12 cm2, 15 cm2 and 20 cm2 respectively, then the volume of the box is

1. 3600 cm³
2. 300 cm³
3. 60 cm³
4. 180 cm³

Correct Option: C

Let the length of rectangular box be l cm.
Width = b cm.
Height = h cm.
According to the question,
lb = 12 sq. cm. bh = 15 sq. cm.
hl = 20 sq. cm.
On multiplying,
l² × b² × h² = 12 × 15 × 20
∴ Volume of box = √12 × 15 × 20
= √3600 = 60 cu. cm.