Question

A rectangular block of metal is 256mm long,152mm wide and 81mm high.if the metal block is melted to form a cube, find the length of each side of the cube.

Answer 1

$\bold\red{\underline{Given:}}$

The length of block of metal=256mm

The breadth of block of metal=152mm

The height of block of metal=81mm

$\bold\green{\underline{Find-Side\:of\:cube:}}$

$\bold\orange{\underline{Solution:}}$

By using formula of volume of cuboid

$\bold\purple{\boxed{Volume=l*b*h}}$

⟹Volume=256*152*81

⟹Volume=3,151,872mm³

Now, using formula of volume of cube

$\bold\purple{\boxed{Volume=Side^3}}$

⟹Volume of cube=volume of cubiod

⟹Side³=Volume of cubiod

⟹Side³=3151872

⟹Side=³√3151872

⟹Side=146.61 mm

Hence,

The length of each side of cube is 146.61 mm

Answer 2

Given:

➺ A rectangular block(cuboid) of metal which is 256mm long,152mm wide and 81mm high

➺ Given block is melted to form a cube

To Find:

• Length of side of the cube

Solution:

We know that,

$\boxed{\sf\pink{Volume\:of\:Cuboid=length\times breadth\times height}}$

$\boxed{\sf\blue{Volume\:of\:Cube=(Side)^{3}}}$

Now,

$\sf{Volume\:of\:Rectangular\:Block=256\times 152\times 81}$

$\sf{Volume\:of\:Rectangular\:Block=3151872\:mm^{3}}$

Let the length of the side of the so formed cube be 'a'.

So,

Volume of Cube= a³

Also, we know that on melting an object and recasting it into new shape does not affect the volume or volume remains the same

i.e. Initial Volume= Final Volume

In this case,

$\bf{Initial\:Volume=Volume\:of\:Rectangular\:Block}$

$\bf{Final\:Volume=Volume\:of\:Cube}$

Therefore,

$\sf{Volume\:of\:Rectangular\:Block=Volume\:of\:Cube}$

3151872= a³, or

a³= 3151872

a= ∛3151872

a= 146.61 mm

Hence, the length of each side of cube is 146.61 mm.