A solid cube of metal each of whose sides measures 2.2 cm is melted to form a cylindrical wire of radius 1 mm. find the length of the wire so obtained.

Answer

To solve the problem, we need to find the length of a cylindrical wire formed by melting a cube of metal. Here are the steps to find the solution:

### Step 1: Calculate the Volume of the Cube
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of a side of the cube.

Given that each side of the cube measures \( 2.2 \) cm, we can calculate the volume as follows:
\[ V = (2.2 \, \text{cm})^3 = 2.2 \times 2.2 \times 2.2 \]
Calculating this:
\[ V = 2.2 \times 2.2 = 4.84 \, \text{cm}^2 \]
\[ V = 4.84 \times 2.2 = 10.648 \, \text{cm}^3 \]

### Step 2: Set Up the Volume of the Cylinder
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height (or length) of the cylinder.

### Step 3: Convert the Radius to Centimeters
The radius of the cylindrical wire is given as \( 1 \) mm. We need to convert this to centimeters:
\[ 1 \, \text{mm} = \frac{1}{10} \, \text{cm} = 0.1 \, \text{cm} \]
So, \( r = 0.1 \, \text{cm} \).

### Step 4: Substitute the Known Values into the Cylinder Volume Formula
Now we can substitute the values into the cylinder volume formula:
\[ 10.648 = \pi (0.1)^2 h \]
\[ 10.648 = \pi (0.01) h \]
\[ 10.648 = 0.01 \pi h \]

### Step 5: Solve for the Height (Length) of the Cylinder
To find \( h \), we rearrange the equation:
\[ h = \frac{10.648}{0.01 \pi} \]
Using \( \pi \approx 3.14 \):
\[ h = \frac{10.648}{0.0314} \]
Calculating this gives:
\[ h \approx 338.8 \, \text{cm} \]

### Final Answer
The length of the wire obtained from melting the cube is approximately:
\[ \boxed{338.8 \, \text{cm}} \]