Question

10) Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are
melted and formed into a single cube. Find the diagonal of this cube.​

Answer 1

AnswEr :

• 12√3 cm

GivEn :

• Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are
• melted.
• They are formed into a single cube.

To Find :

• The diagonal of new cube.

Solution :

The formula of volume of cubes,

$\boxed{ \sf{V_{cube} = {a}^{3} }}$

• a = Side of cube

Melting the cubes, we get the total volume of new cube.

• Volume of 1st cube = 6³ = 216 cm³
• Volume of 2nd cube = 8³ = 512 cm³
• Volume of 3rd cube = 10³ = 1000 cm³

Total volume = 216 + 512 + 1000 = 1728 cm³

Now, the side of new cube,

• a³ = 1728
• → a = 12

Therefore, the diagonal is (a√3) = 12√3 cm.

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

Three metal cubes with edges $6\:cm,$ $8\:cm$ and $10\:cm$ respectively are melted and formed into a single cube. Find the diagonal of this cube.

$\huge\bold{\mathbb{GIVEN}}$

• Three metal cubes with edges $6\:cm,$ $8\:cm$ and $10\:cm$ respectively are melted and formed into a single cube.

$\huge\bold{\mathbb{TO\:FIND}}$

The diagonal of the cube.

$\huge\bold{\mathbb{SOLUTION}}$

We know that:

$\boxed{\boxed{Volume_{(Cube)}=a^3\:unit^3}}$

Where, $a$ is the side of the cube.

Putting the formula, let's find out the volume of each cube.

Volume of:

• $1^{st}$ cube $=a^3=6^3\:cm^3=216\:cm^3$

• $2^{nd}$ cube $=a^3=8^3\:cm^3=512\:cm^3$

• $3^{rd}$ cube $=a^3=10^3\:cm^3=1000\:cm^3$

Volume of the new cube

$= V_{(1st\:cube)}+V_{(2nd\:cube)}+V_{(3rd\:cube)}$

$= (216+512+1000)\:cm^3$

$= 1728\:cm^3$

Using the formula, let's find out the side of the new cube.

$a^3=1728$

$\implies a=\sqrt[3]{1728}$

$\implies a=\sqrt[3]{(12\times12\times12)}$

$\implies a=12$

So, side of the new cube $=12\:cm$

We know that:

$\boxed{\boxed{Diagonal_{(Cube)}=\sqrt{3}a\:unit}}$

Where, $a$ is the side of the cube.

Putting the formula, let's find out the diagonal of the cube.

$\sqrt{3}a$

$=\sqrt{3}\times12$

$=12\sqrt{3}$

So, diagonal of the new cube $=12\sqrt{3}\:cm$

$\huge\bold{\mathbb{THEREFORE}}$

The diagonal of the new cube is $12\sqrt{3}\:cm.$

$\huge\bold{\mathbb{WE\:MADE\:IT\:!!}}$