Question

the edges of three cubes are metal are 3cm 4cm and 5cm their metalled and forms in single cube find the edge of the new cube​

Answer 1

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

• Given the edges of 3 cubes

• Now find the volume of 3 cubes

$\boxed{\sf{Volume\:of\:cube=side{}^{3}}}$

$\sf\implies Volume\:of\:cube_1= (3){}^{3}\\ \\ \sf\implies {\pink{Volume\:of\:cube_1= 27cm{}^{3}}}$

Now the volume of 2nd cube

$\sf\implies Volume\:of\:cube_2= (4){}^{3}\\ \\ \sf\implies{\purple{ Volume\:of\:cube_2= 64cm{}^{3}}}$

Now the volume of 3rd cube

$\sf\implies Volume\:of\:cube_3= (5){}^{3}\\ \\ \sf\implies {\blue{Volume\:of\:cube_3= 125cm{}^{3}}}$

Now they together melted and form new cube

$\boxed{\sf{Volume\:of\:new\: cube=V.\:of\:cube_1+V.\:of\:cube_2+V.\:of\:cube_3}}$

$\sf\implies Volume\:of\:new\:cube= 27+64+125\\ \\ \sf\implies Volume\:of\:new\:cube= 216\\ \\ \sf\implies Volume\:of\:new\:cube= 216cm{}^{3}$

Now the side/edge of cubeSide=cube root of volume

$\sf\implies side\:of\:cube=\sqrt[3]{216} \\ \\ \sf\implies Side\:of\:cube= 6cm$

$\boxed{\sf{edge\:of\:cube=}{\mathfrak{\red{6cm}}}}$

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=$\mathsf {{a}^{3}}$

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

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