Question

The dimensions of a metallic cuboid are:\[ 100 \times 80 \times 64\] .It is melted into a cube. Find the surface area of a cube.

Answer 1

Hint: As we know in the question it is given dimensions of a metallic cuboid. It is a three-dimensional structure, a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. It has a length, width & height. Each face of the cuboid is a rectangle that is 90-degree angled. Also, each face of the cube is a square and is 90-degree angled. We could find the volume of cuboid as the volume of the cube will be equal to the volume of cuboid after melting.

Given: The dimensions of a metallic cuboid which is recast, length = 100cm, breadth = 80cm and height = 64cm.It is recast into a cube by melting the metal and in this question, we have to find out the surface area of the cube.

Complete step-by-step answer:
Volume of a cuboid is equal to multiply of length, width and height.
Volume of a cuboid = \[100 \times 80 \times 64 = 512000c{m^3}\]
As, it is recast into a cube, volume of cube = volume of cuboid.
Volume of the cube is equal to multiplication of its side twice.
As, volume of cube = side × side × side
\[\
   \Rightarrow 512000 = {(side)^3} \\
   \Rightarrow {(80)^3} = {(side)^3} \\
   \Rightarrow side = 80cm \\
 \]

Each side of cube is equal to 80cm
The total surface area of the cube is equal to 6 side by side.
As, Total surface area of cube = \[ = 6 \times side \times side\]
We will put the value of the side of the cube.
Total surface area = \[6 \times 80 \times 80 = 38400c{m^2}\]

Note: In these types of questions we can find out the volume and surface area of all other geometrical shapes as well by putting the volume of recast shapes equal. Other geometrical shapes may be cylinder, cone etc