Question

A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Answer 1

let n boxes are placed in the given cuboid .
volume of cuboid =n x volume of cube
60 x 54 x 30 = n x (6)^3

n=60 x 54 x 30/6 x 6 x 6

=10 x 9 x 5 =450
hence 450 boxes are placed in the cuboid

Answer 2

length of cuboid , l = 60 cm
breadth , b = 54 cm
height , h =30 cm
Volume of cuboid = lbh
= 60 × 54 × 30
= 97200 cm ³

side of a cube , a = 6 cm
Volume of 1 cube = a³ = 6 × 6 × 6 = 216 cm³


No: of cubical boxes that can be placed in the cuboid = Volume of cuboid ÷ Volume of 1 cube
= 97200 cm ³ ÷ 216 cm³
= 450 boxes


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