Question

A metallic cuboid’s dimensions are 10 cm, 27 cm and 12.5 cm. It is melted and recast into a cube. Find (i) the edge of the cube and (ii) the total surface area of the cube.

Answer 1

Given:

• Dimensions of the metallic cuboid:
  • Length L = 10cm
  • Width W = 27cm
  • Height H = 12.5 cm

When the cuboid is melted and recast into a cube, we can find the edge of the cube by using the volume of the cuboid.

Step 1: Calculate the volume of the cuboid

The volume of a cuboid is given by the formula:

Volume of the cuboid = L × W × H

Volume of the cuboid = 10 cm × 27 cm × 12.5 cm = 3,375 cm³ 

Step 2: Calculate the edge of the cube

Since the volume of the cuboid is melted and recast into a cube, the volume of the cube will be the same as the volume of the cuboid.

The volume of a cube is given by: 

Volume of the cube = Edge³

Let the edge of the cube be a.

So, we have:

a³ = 3,375

Taking the cube root of both sides:

`a = root(3)(3,375) = 15` cm

Step 3: Calculate the total surface area of the cube

The total surface area of a cube is given by the formula:

Surface area of the cube = 6a²

Substituting a = 15 cm:

Surface area of the cube = 6 × 15²

= 6 × 225

= 1,350 cm²