Question

Three cubes of sides 3 cm, 4cm and 5 cm are melted and a new cube is formed. Find the edges of new cube

Answer 1

Answer:

• Edge of new cube = 6 cm

Step-by-step explanation:

Given:

• Side of 1st cube = 3 cm
• Side of 2nd cube = 4 cm
• Side of 3rd cube = 5 cm

To Find:

• Edge of new cube formed by these three cubes.

$\rule{200}{2}$

Now, we will calculate volume of these three cubes,

⇒ Volume of 1st cube = a³

⇒ Volume of 1st cube = 3³

⇒ Volume of 1st cube = 27 cm³

$\rule{200}{2}$

⇒ Volume of 2nd cube = a³

⇒ Volume of 2nd cube = 4³

⇒ Volume of 2nd cube = 64 cm³

$\rule{200}{2}$

⇒ Volume of 3rd cube = a³

⇒ Volume of 3rd cube = 5³

⇒ Volume of 3rd cube = 125 cm³

$\rule{200}{2}$

Now, we will calculate total volume of three cubes,

⇒ Total Volume = 27 + 64 + 125

⇒ Total Volume = 216 cm³

$\rule{200}{2}$

Now, we know that,

⇒ Volume of new cube = 216 cm³

⇒ a³ = 216

⇒ a = 6 cm.

$\rule{200}{2}$

Hence, Edge of new cube = 6 cm

Answer 2

Question :

Three cubes of sides 3 cm, 4cm and 5 cm are melted and a new cube is formed. Find the edges of new cube.

To Find :

Edges of the new cube

Answer :

Answer of your question is 6 cm

Step by Step explanation :

Given:

Side of the 1st cube: 3 cm

Side of the 2nd cube: 4 cm

Side of the 3rd cube: 5 cm

Let us find the volume of the respective cubes,

Volume of the first cube: $\mathsf {27\:{cm}^{3}}$

Volume of the second cube: $\mathsf { 64\:{cm}^{3}}$

Volume of the third cube: $\mathsf {125\:{cm}^{3}}$

We get the total volume as:

$:\implies \mathsf {27 + 64 + 125}$

$:\implies \mathsf {216\:{cm}^{3}}$

Then the side of the new cube will be=$\mathsf {{a}^{3}}$

$:\implies \mathsf {{a}^{3}= 216\:{cm}^{3}}$

$:\implies \mathsf {6\:cm}$