Question

a solid piece of metal in the form of a cuboid of dimensions 24cm ×18cm * 4cm is melted down and recasted into a cube. find the length of each edge of the cube

Answer 1

There is a cuboid of dimensions 24cm x 18cm x 4cm

Volume of cuboid = length X breadth X height

= 24 X 18 X 4

=1728cm cube.

the cuboid is melted down and recasted into a cube

but the volume remains same

volume of cube = volume of cuboid

side^3 = 1728

side = 12

hence each edge of the cube is 12cm.

Answer 2

The edge of the cube is 12cm.

Given:

Dimensions of Cuboid = 24cm × 18cm × 4cm.

To Find:

The length of each edge of the Cube.

Solution:

Here, it is given that the dimensions of the Cuboid are

Length of the Cuboid $=24cm$

The breadth of the Cuboid $=18cm$

Height of the Cuboid $=4cm$.

now, we know that,

Volume of Cuboid $=length\times breadth\times height$

here, after putting the given values in the above formula,

we get,

Volume of Cuboid $=24\times 18\times 4$

                               $=1728cm^{3}$

we get, the volume of Cuboid $=1728cm^{3}$.

Now, the volume of the cube = volume of the cuboid

here we get,

$(a)^{3} =1728$

now, $a=12cm$.

Thus, the edge of the cube is 12cm.