Question

A solid cube of edge 7.5 cm. is melted and recasted into smaller cubes cach of edge 1.25 cm. How many number of smaller cubes are recasted?​

Answer 1

Given :-

• A solid cube of edge 7.5 cm. is melted and recasted into smaller cubes cach of edge 1.25 cm

To find :-

• Number of resultant smaller cubes .

Solution :-

Given that

The edge of a cube = (a) = 7.5 cm

We know that

The Volume of a cube is 'a³' cubic units .

Volume of the cube = (7.5)³ cm³

=> Volume = 7.5×7.5×7.5 cm³

=> Volume = 421.875 cm³

If the cube is melted then it recasted into cubes

The edge of the smaller cube = 1.25 cm

Volume of the smaller cube = (1.25)³ cm³

=> Volume = 1.25×1.25×1.25 cm³

=> Volume = 1.953125 cm³

Let the number of smaller cubes are formed be X

Total volume of X smaller cubes =1.953125X cm³

We know that

If a solid is melted and recast into another solid then the volume of the original solid is equal to the volume of the resultant solid.

=> 1.953125X = 421.875

=> X = 421.875/1.953125

=> X = 216

Therefore, X = 216

The number of solids = 216

Answer :-

• The required number of smaller cubes is 216

Used formulae:-

• The Volume of a cube is 'a³' cubic units .

• a = Edge of the cube

Used Concept :-

• If a solid is melted and recast into another solid then the volume of the original solid is equal to the volume of the resultant solid.

Answer 2

Answer:

Given :-

• A solid cube of edge 7.5 cm is melted and recasted into smaller cubes each of edge 1.25 cm.

To Find :-

• How many number of smaller cubes are recasted.

Solution :-

First, we have to find the volume of bigger cube :

Given :

• Edge = 7.5 cm

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{Volume_{(Cube)} =\: (Edge)^3}}$

So,

$\implies \bf Volume_{(Bigger\: Cube)} =\: (Edge)^3$

$\implies \sf Volume_{(Bigger\: Cube)} =\: (7.5)^3$

$\implies \sf Volume_{(Bigger\: Cube)} =\: (7.5 \times 7.5 \times 7.5)$

$\implies \sf Volume_{(Bigger\: Cube)} =\: (56.25 \times 7.5)$

$\implies \sf\bold{\underline{Volume_{(Bigger\: Cube)} =\: 421.875\: cm^3}}$

Now, we have to find the volume of smaller cube :

Given :

• Edge = 1.25 cm

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{Volume_{(Cube)} =\: (Edge)^3}}$

So,

$\implies \bf Volume_{(Smaller\: Cube)} =\: (Edge)^3$

$\implies \sf Volume_{(Smaller\: Cube)} =\: (1.25)^3$

$\implies \sf Volume_{(Smaller\: Cube)} =\: (1.25 \times 1.25 \times 1.25)$

$\implies \sf Volume_{(Smaller\: Cube)} =\: (1.5625 \times 1.25)$

$\implies \sf\bold{\underline{Volume_{(Smaller\: Cube)} =\: 1.953125\: cm^3}}$

Now, we have to find how many number of smaller cubes and recasted :

Given :

• Volume Of Bigger Cube = 421.875 cm³
• Volume Of Smaller Cube = 1.953125 cm³

According to the question by using the formula we get,

$\footnotesize \dashrightarrow \sf\boxed{\bold{Number\: of\: Smaller\: Cube =\: \dfrac{Volume_{(Bigger\: Cube)}}{Volume_{(Smaller\: Cube)}}}}$

$\dashrightarrow \sf Number\: of\: Smaller\: Cube =\: \dfrac{421.875}{1.953125}$

$\dashrightarrow \sf\bold{\underline{Number\: of\: Smaller\: Cube =\: 216}}$

$\therefore$ The number of smaller cubes are recasted is 216 .