Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is

Options

A. 12 cm
B. 14 cm
C. 16 cm
D. 18 cm

Answer

To find the edge of the new cube formed by melting three smaller cubes with edges of 6 cm, 8 cm, and 10 cm, we will follow these steps:

### Step-by-Step Solution:

1. **Calculate the Volume of Each Cube:**
- The volume \( V \) of a cube is given by the formula \( V = a^3 \), where \( a \) is the edge length of the cube.
- For the first cube with edge 6 cm:
\[ V_1 = 6^3 = 6 \times 6 \times 6 = 216 \, \text{cm}^3 \]
- For the second cube with edge 8 cm:
\[ V_2 = 8^3 = 8 \times 8 \times 8 = 512 \, \text{cm}^3 \]
- For the third cube with edge 10 cm:
\[ V_3 = 10^3 = 10 \times 10 \times 10 = 1000 \, \text{cm}^3 \]

2. **Calculate the Total Volume of the New Cube:**
- The total volume \( V_{total} \) of the new cube formed by melting the three smaller cubes is the sum of their volumes:
\[ V_{total} = V_1 + V_2 + V_3 = 216 + 512 + 1000 = 1728 \, \text{cm}^3 \]

3. **Determine the Edge Length of the New Cube:**
- Let the edge length of the new cube be \( A \). The volume of the new cube can also be expressed as \( A^3 \).
- Therefore, we have:
\[ A^3 = V_{total} = 1728 \]
- To find \( A \), we take the cube root of 1728:
\[ A = \sqrt[3]{1728} \]

4. **Calculate the Cube Root:**
- We can find the cube root of 1728:
\[ A = 12 \, \text{cm} \]

### Final Answer:
The edge of the new cube formed is **12 cm**.

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