Question

A cuboid of dimensions 64cm × 48cm × 24cm. How many small cubes with side 8cm can be placed in the given cuboid

Answer 1

Volume of big cuboid = lbh = 64 × 48 × 24

= 73728cm²

Volume of small cubes = a³ = 8³ = 512cm²

No.of cubes that can fit in the cuboid = 73728/512 = 144

Hope it helps you......

Answer 2

144 small cubes with the side of 8 cm can be placed in the given cuboid.

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Let's understand a few concepts:

We can calculate the volume of a cuboid by using the following formula:

$\boxed{\bold{Volume\:of\:a\:cuboid = length \times breadth \times height}}$

We can calculate the volume of a cube by using the following formula:

$\boxed{\bold{Volume\:of\:a\:cuboid = side^3}}$

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Let's solve the given problem:

For Cuboid:

Length = 64 cm

Breadth = 48 cm

Height = 24 cm

∴ Volume of the cuboid = L × B × H = 64 × 48 × 24 = 73728 cm³

For Cube:

Side, a = 8 cm

∴ Volume of 1 small cube = a³ = 8³ = 512 cm³

Now,

The required no. of such small cubes with a side of 8 cm that can be placed in the cuboid is,

= $\frac{Volume\:of\:cuboid}{Volume \:of\:cube}$

= $\frac{73728\:cm^3}{512\:cm^3}$

= $\bold{144}$

Thus, 144 small cubes with a side of 8cm can be placed in the given cuboid.

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