Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is

Options

A. 12 cm
B. 24 cm
C. 18 cm
D. 20 cm

Answer

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

### Step 1: Calculate the volume of each cube.
The volume \( V \) of a cube is given by the formula:
\[ V = \text{edge}^3 \]

- For the cube with edge 6 cm:
\[ V_1 = 6^3 = 216 \, \text{cm}^3 \]

- For the cube with edge 8 cm:
\[ V_2 = 8^3 = 512 \, \text{cm}^3 \]

- For the cube with edge 10 cm:
\[ V_3 = 10^3 = 1000 \, \text{cm}^3 \]

### Step 2: Find the total volume of the three cubes.
Now, we sum the volumes of the three cubes:
\[ \text{Total Volume} = V_1 + V_2 + V_3 = 216 + 512 + 1000 \]
\[ \text{Total Volume} = 1728 \, \text{cm}^3 \]

### Step 3: Set up the equation for the new cube.
Let \( A \) be the edge of the new cube formed by melting the three cubes. The volume of the new cube is also given by:
\[ V = A^3 \]
Thus, we have:
\[ A^3 = 1728 \, \text{cm}^3 \]

### Step 4: Solve for \( A \).
To find \( A \), we take the cube root of both sides:
\[ A = \sqrt[3]{1728} \]

Calculating the cube root:
\[ A = 12 \, \text{cm} \]

### Conclusion:
The edge of the new cube formed by melting the three cubes is **12 cm**.

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