Question

If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm²and 25 cm³. Find the vlume of the cuboid.

Answer 1

Given :  Areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm².  

Let the dimensions of cuboid be l, b and h .  

Let these adjacent faces of a cuboid are x, y ,z .

x = lb = 8 , y = bh = 18 , z = hl = 25

and volume of cuboid = V  

V = lbh

On squaring both sides :  

V² = (lbh)² = l²b²h²

V² = lb × bh × hl

V² = xyz

V = √xyz

V = √(8 × 18 × 25)

V = √3600

V = 60 cm³

Hence, the volume of the cuboid is 60 cm³.

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Answer 2

Given:

Areas of three adjacent faces of a cuboid: 8 sq cm, 18 sq cm, 25 sq cm

To find:

The volume of the cuboid

Solution:

Let the dimensions of the cuboid be = l, b, h

lb = 8

bh = 18

lh = 25

Volume of a cuboid = lbh

Multiply all the 3 equations above:

lb × bh × lh = 8 × 18 × 25

=> (lbh)^2 = 3600

=> lbh = √3600

=> lbh = 60 cu cm