A cuboid with dimensions 2 x 4 x 1 units is melted and a new cube is made. what is the total surface area of the cube formed in square units?

To find the total surface area of the cube formed, we need to go through the following steps:

1. **Calculate the volume of the cuboid**:
   The volume \( V \) of the cuboid is given by:
   \[
   V = \text{length} \times \text{width} \times \text{height}
   \]
   Given the dimensions of the cuboid as \( 2 \times 4 \times 1 \) units, the volume is:
   \[
   V = 2 \times 4 \times 1 = 8 \, \text{cubic units}
   \]

2. **Determine the side length of the cube**:
   Since the melted cuboid is reformed into a cube, the volume of the cube is the same as the volume of the cuboid. Let the side length of the cube be \( s \). The volume \( V \) of the cube is given by:
   \[
   V = s^3
   \]
   Equating the volume of the cube to the volume of the cuboid:
   \[
   s^3 = 8
   \]
   Solving for \( s \):
   \[
   s = \sqrt[3]{8} = 2
   \]
   So, the side length of the cube is \( 2 \) units.

3. **Calculate the total surface area of the cube**:
   The surface area \( A \) of a cube is given by:
   \[
   A = 6s^2
   \]
   Substituting \( s = 2 \):
   \[
   A = 6 \times (2^2) = 6 \times 4 = 24 \, \text{square units}
   \]

Thus, the total surface area of the cube is **24 square units**.

Would you like more details on any part of the solution?

Here are some related questions:
1. What is the surface area of the cuboid before melting?
2. How does surface area differ from volume in these shapes?
3. Can other solids with the same volume have the same surface area?
4. How would the result change if the cuboid had different dimensions?
5. What if a cylinder was formed instead of a cube?

**Tip**: Always remember, the volume remains the same when an object is melted and reshaped, but the surface area changes based on the new shape.

A cuboid with dimensions 2 x 4 x 1 units is melted and a new cube is made. What is the total surface area of the cube formed in square units?

Discover how to find the total surface area of a cube formed by melting a cuboid with dimensions 2 x 4 x 1 units. Learn the concepts of volume, cubic roots, and surface area with a detailed solution, suitable for students in Grades 6-8.

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