Twelve solid spheres of the same sizes are made by melting a solid metallic cylinder of base diameter 2 cm and height 16cm. Find the radius of each sphere.

Answer

To solve the problem of finding the radius of each sphere formed by melting a solid metallic cylinder, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the cylinder:**
- The base diameter of the cylinder is given as 2 cm.
- Therefore, the radius \( R \) of the cylinder is:
\[ R = \frac{\text{Diameter}}{2} = \frac{2 \text{ cm}}{2} = 1 \text{ cm} \]
- The height \( h \) of the cylinder is given as 16 cm.

2. **Calculate the volume of the cylinder:**
- The formula for the volume \( V \) of a cylinder is:
\[ V = \pi R^2 h \]
- Substituting the values:
\[ V = \pi (1 \text{ cm})^2 (16 \text{ cm}) = \pi \times 1 \times 16 = 16\pi \text{ cm}^3 \]

3. **Set up the equation for the volume of the spheres:**
- We know that the volume of 12 spheres is equal to the volume of the cylinder.
- The formula for the volume of one sphere is:
\[ V_{\text{sphere}} = \frac{4}{3} \pi r^3 \]
- Therefore, the volume of 12 spheres is:
\[ V_{\text{12 spheres}} = 12 \times \frac{4}{3} \pi r^3 = 16\pi \text{ cm}^3 \]

4. **Equate the volumes:**
- Setting the volume of the cylinder equal to the volume of the spheres:
\[ 16\pi = 12 \times \frac{4}{3} \pi r^3 \]

5. **Simplify the equation:**
- Cancel \( \pi \) from both sides:
\[ 16 = 12 \times \frac{4}{3} r^3 \]
- Simplifying further:
\[ 16 = 16 r^3 \]

6. **Solve for \( r^3 \):**
- Divide both sides by 16:
\[ r^3 = 1 \]

7. **Find the radius \( r \):**
- Taking the cube root of both sides:
\[ r = \sqrt[3]{1} = 1 \text{ cm} \]

### Final Answer:
The radius of each sphere is **1 cm**.