Question

How many cuboids of side 6cm,3cm and 6cm will be needed to form a cube of side 6cm

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

AnswEr:

• The number of cuboids needed to form a cube = 2.

Given Information:

Dimensions of cuboid,

• Length = 6
• Breadth = 3
• Height = 6
• Side of cube = 6

Need To Find:

• The number of cuboids needed to form a cube = ?

ExPlanation:

In Case 1:

Given That:

• The dimensions of cuboid = 6 × 3 × 6.

Need To Find:

• The area of cuboid = ?

Formula used here:

• Area of cuboid = Length × Breadth × Height

Putting the values according to the given formula:

➠ Area of cuboid = 6 × 3 × 6

➠ Area of cuboid = 108

Hence:

• The area of cuboid is 108 cm³.

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In Case 2:

Need To Find:

• The area of cube = ?

Formula used here:

• Area of cube = Side × Side × Side

➠ Area of cube = 6 × 6 × 6

➠ Area of cube = 216

Hence:

• The area of cube is 216 cm³.

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In Case 3:

• The number of cuboid needed to form a cube = Area of cube/Area of cuboid

Now, putting the values:

Cuboid needed to form a cube = $\mathsf {\dfrac{\cancel{216}}{\cancel{108}}}$

Cuboid needed to form a cube = 2

Hence:

• The number of cuboid needed to form a cube is 2.

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Answer 2

Given :

• Length of cuboid = 6 cm.

• Breadth of cuboid = 3 cm.

• Height of cuboid = 6 cm.

• Sides of cube = 6 cm.

To find :

• Number cuboids of side 6cm,3cm and 6cm will be needed to form a cube of side 6cm =?

Step-by-step explanation :

Dimensions of cuboid = 6 × 3 × 6 . [Given]

We know that,

Volume of cuboid = length x breadth x height

Substituting the values in the above formula, we get,

= 6 × 3 × 6

= 108.

Therefore, Volume of cuboid = 108 cm³.

Now,

We have to find the Volume of cube,

We know that,

Volume of cube = side³.

Substituting the values in the above formula, we get,

= 6³ [ Side of cube = 6 cm]

= 6 × 6 × 6

= 216.

Therefore, Volume of cube = 216 cm³.

Now,

Number cuboids will be needed to form a cube = Volume of cube / Volume of cuboid.

Substituting the values, we get,

= 216/108

= 2.

Therefore, 2 cuboids will be needed to form a cube.