Question

the areas of three adjacent faces of a cuboidal box are 120 cm sq. 72cm sq. and 60 cm sq. respectively find the volume of box

Answer 1

area of 3 faces = lb + bh + lh
so, 120 = lb
        72 = bh
        60 = lh
multiply all three
l²b²h² = 518400
so, lbh =√518400 = 720 cm³

Answer 2

Answer:

Volume of the Cuboidal Box (V) = 720cm³

Step-by-step explanation:

Dimensions of the Cuboidal Box:

Let Length = l cm,

breadth = b cm,

height = h cm

According to the problem given,

Areas of three adjacent faces are,

lb = 120 cm² ----(1)

bh = 72 cm² -----(2)

lh = 60 cm² ------(3)

Multiply equations (1),(2)& (3) ,we get

lb × bh × lh = 120cm²×72cm²×60

=> (l²b²h²) = (12×10×12×6×6×10)

=> (lbh)² = (12×6×10cm³)²

=> √(lbh)² = √(12×5×10cm³)²

=> lbh = 720 cm³

Volume of the Cuboidal Box (V) = lbh = 720cm³

Therefore,

Volume of the Cuboidal Box (V) = 720cm³

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