Question

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

Answer 1

Answer:

12 cm

Step-by-step explanation:

The above solid is in the form of cuboid before melting

Volume of a cuboid = length × breadth × height

Volume of the given cuboid = 24×18×4 = 1728 cm^3

As the cuboid is melted into the cube, the volume will remain constant

Volume of cube = side^3

1728 = a^3

a = 12

The length of the edge of the cube is 12 cm

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Answer 2

Question :

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

Solution :

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

• Dimensions of cuboid= 24 cm×18 cm× 4 cm

$\underline{\bold {To\:Find:}}$

• The length of each edge of cube.

Metal in the form of cuboid into recasted into Cube.

$\therefore {Volume\: of\: Cube =Volume \:of \:Cuboid}$

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

$\implies Volume \: of \: Cuboid=length \times breadth \times height \\ \implies Volume \: of \: Cuboid = 24 \: cm \times 18 \: cm \times 4 \: cm \\ \implies Volume \: of \: Cuboid = 1728 \: {cm}^{3}$

$\therefore {Volume \:of\:cube=1728 \: {cm}^{3}}$

$\boxed {\pink {Each\:edge \:of \:cube = \sqrt[3]{Volume}}}$

$\implies Edge = \sqrt[3]{Volume}\\\implies Edge = \sqrt[3]{1728}\:cm\\\implies Edge = \sqrt[3]{12\times 12\times 12}\:cm\\\implies Edge =12 \:cm$

$\fbox {\green{The\:length\: of\:each\:edge \:of \:cube =12 \:cm}}$

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