Question

Three cuboids of dimensions 2 cm ⨉ 5 cm ⨉ 7 cm, 4 cm ⨉ 3 cm ⨉ 5 cm and 2 cm ⨉ 3 cm ⨉ 11 cm are melted and a cube is formed. Find the side of the cube.​

Answer 1

Given :-

1. There are 3 cuboids of dimensions ::  

• Cuboids ( i ) – 2 cm , 5 cm , 7cm  

• Cuboids ( ii ) – 4 cm, 3 cm , 5 cm  

• Cuboids ( iii ) – 2 cm , 3 cm , 11 cm  

To Find :-

• Side of the cube if all these cuboids are melted to form one.  

Solution :-

~Here, firstly we’ll find volume of each of the cuboid by applying the formula ( lbh ) and total them to form volume of all melted cuboids. The volume of all melted cuboids will be equal to the volume of the new cube formed. We can find the side of that new cube formed by putting the values in formula of it’s volume.  

As we know that ,

$\sf \maltese \;\; Volume\;of\;cuboid = l \times b \times h$

$\sf \maltese \;\; Volume\;of\;Cube = (side)^{3}$

Finding the total volume ::

→ Volume of Cuboid ( i )

$\sf \implies 2\;cm \times 5\;cm \times 7\;cm$  

$\sf \implies 70\;cm^{3}$

→ Volume of Cuboid ( ii )  

$\sf \implies 4\;cm \times 3\;cm \times 5\;cm$  

$\sf \implies 60\;cm^{3}$

→ Volume of Cuboid ( iii )  

$\sf \implies 2\;cm \times 3\;cm \times 11\;cm$ 

$\sf \implies 66\;cm^{3}$

$\sf \bullet \;\; Total\;Volume = ( 60 + 70 + 66 ) = 196\;cm^{3}$

Finding the Side of the Cube ::  

$\sf \implies (side)^{3} = 196\;cm^{3}$

$\sf \implies side =$  $\sf \sqrt[3]{196}$

$\sf \implies side = 5.808\;cm$

Hence,

• Side of the cuboid will be 5.808 cm  

Answer 2

Given :

Three cuboids of dimensions 2 cm × 5 cm × 7 cm, 4 cm × 3 cm × 5 cm and 2 cm × 3 cm × 11 cm are melted and a cube is formed.

To find :

Find the side of the cube.

Solution :

Let Cuboids

2 cm × 5 cm × 7 cm.

4 cm × 3 cm × 5 cm

2 cm × 3 cm × 11 cm

Volume of Cuboid = L × B × H

Volume of Cube = ( Side )³

Volume of cuboid ( 1 )

= 2 cm × 5 cm × 7 cm.

= 70 cm³

Volume of Cuboid ( 2 )

= 4 cm × 3 cm × 5 cm

= 60 cm³

Volume of Cuboid ( 3 )

= 2 cm × 3 cm × 11 cm

= 66 cm³

Volume of Three cuboids = ( 70 + 60 + 66 )

= 196 cm³

Volume Of cube

( Side )³ = 196 cm³

Side = ∛196

= 5.808 cm