Question

A metal sheet 32 cm long, 8 cm broad and 2 cm thick is melted into a cube. The side of the cube is ________.

Answer 1

Answer:

The cube has a side of 8 cm.

Step-by-step explanation:

The volume of the metal sheet and the cube will be the same.

The metal sheet has the measurements,

$length=32 \ cm\\\\breadth =8\ cm\\\\thickness = 2\ cm$

So the volume of the metal sheet is,

$Volume = length\times breadth\times thickness = 32\times 8\times 2 = 512\ cm^3$

Let $a$ be the side of the cube. So the volume is,

$volume = a^3$

Since the volume of the metal sheet and cube are the same, we can equate the volume. So

$\implies a^3=512\\\\\implies a=\sqrt[3]{512}=8 \ cm$

Thus the cube has a side of 8 cm.

Answer 2

Answer:

Given :-

• A metal sheet 32 cm long, 8 cm broad and 2 cm thick is melted into a cube.

To Find :-

• What is the side of the cube.

Solution :-

First, we have to find the volume of sheet :

Given :

• Length = 32 cm
• Breadth = 8 cm
• Height = 2 cm

According to the question by using the formula we get,

$\footnotesize \implies \sf\boxed{\bold{\pink{Volume_{(Sheet)} =\: Length \times Breadth \times Height}}}$

By putting the values we get,

$\implies \sf Volume_{(Sheet)} =\: 32\: cm \times 8\: cm \times 2\: cm$

$\implies \sf Volume_{(Sheet)} =\: 256\: cm^2 \times 2\: cm$

$\implies \sf\bold{\purple{Volume_{(Sheet)} =\: 512\: cm^3}}$

Now, we have to find the side of the cube :

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

where,

• a = Side of the cube

According to the question by using the formula we get,

$\implies \bf a^3 =\: 512$

$\implies \sf a =\: \sqrt[3]{512}$

$\implies \sf\bold{\red{a =\: 8\: cm}}$

$\therefore$ The side of the cube is 8 cm .