Question

How many small cubes with side of 2cm can accommodate in a cubical box of 8 cm side? with full explaination​

Answer 1

Answer:

Mark as brainliest answer.

Step-by-step explanation:

→ Small cubes with side of 2 cm

→ volume of cubical box of side 8 cm

→ 8³ = 512 cm³

→ volume of small cubes = 2³ = 8

→ 512 / 8 = 64

→ ∴ 64 small cubes with side of 2 cm can accommodate in a cubical box of 8 cm .

Answer 2

Given,

Side of cube 1 ($a_{1}$) = 2 cm

Side of cube 2 ($a_{2}$) = 8 cm

To find,

The number of small cubes that can fit into the larger cube.

Solution,

In order to solve the given question easily and correctly, we can follow the given steps.

From the knowledge, we have of this chapter in Mathematics we know that,

Area of a cube = 6 $a^{2}$

To solve this question we will have to calculate the area of both cubes.

Area of cube 1:

A1 = 6 $a_{1} ^{2}$

A1 = 6 × $2^{2}$

A1 = 24 $cm^{2}$

So, the area of the smaller cube is 24 $cm^{2}$.

Area of cube 2:

A2 = 6 $a_{2} ^{2}$

A2 = 6 × $8^{2}$

A2 = 384 $cm^{2}$

So, the area of the larger cube is 384 $cm^{2}$.

Now, for us to calculate the number of smaller cubes that can fit into the larger one we need to divide the areas of both the cubes.

The number of smaller cubes that can fit into the larger cube:

= area of cube 2 ÷ area of cube 1

= $\frac{384}{24}$    

= 16

Hence, we can accommodate 16 smaller cubes into the cube of side 8cm.