Question

A cube of side 60m can accommodate some smaller cubes of side 2m .How many small cubes can be placed in the given cube?

Answer 1

⇒ Given:

A hollow cube of side 60 m.

Some smaller cubes of side 2 m.

⇒ To Find:

The number of cubes that can be filled in.

⇒ Solution:

The basic concept to be used in this question is the volume of a cube with the formula:

$\bf{Volume\:of\:cube=a^3}$

First, we need to find the volume of the larger cube and then the volume of one smaller cube. Dividing these values, we will get the number of cubes.

Side of bigger cube = 60 m

Formula to find the volume = a³

Volume of the larger cube = 60³

Volume of the larger cube = 216000 m³

Now,

Side of one smaller cube = 2 m

Formula to find the volume = a³

Volume of one smaller cube = 2³

Volume of one smaller cube = 8 m³

Number of smaller cubes that can be stored in the large cube:

$\sf{\dfrac{Volume\:of\:large\:cube}{Volume\:of\:one\:small\:cube}}$

$\sf{=\dfrac{216000}{8}}$

$\sf{=27000}$

∴ 27000 cubes can be stored.

Formulae related to a cube:

→ LSA = 4a²

→ TSA = 6a²

→ Volume = a³