The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 cm. The length of the wire is.

Answer

To find the length of the wire formed by melting a sphere, we need to follow these steps:

### Step 1: Calculate the Volume of the Sphere
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.

**Given:**
- Diameter of the sphere = 6 cm
- Radius \( r = \frac{6}{2} = 3 \) cm

**Calculating the volume:**
\[ V = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36 \pi \text{ cm}^3 \]

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

**Given:**
- Diameter of the wire = 2 cm
- Radius \( r = \frac{2}{2} = 1 \) cm

### Step 3: Set the Volume of the Sphere Equal to the Volume of the Cylinder
Since the sphere is melted and transformed into the wire, their volumes are equal:
\[ 36 \pi = \pi (1)^2 h \]

### Step 4: Simplify the Equation
We can cancel \( \pi \) from both sides:
\[ 36 = 1^2 h \]
\[ 36 = h \]

### Step 5: Conclusion
The length of the wire is:
\[ h = 36 \text{ cm} \]

### Final Answer
The length of the wire is **36 cm**.

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