The suface area of a solid metallic sphere is 2464 `cm^(2)`. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate :
(i) the radius of the sphere.

Answer

To find the radius of the sphere given its surface area, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the surface area of a sphere**:
The surface area \( A \) of a sphere is given by the formula:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.

2. **Set up the equation with the given surface area**:
We know the surface area of the sphere is \( 2464 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 4\pi r^2 = 2464 \]

3. **Substitute the value of \( \pi \)**:
For this calculation, we can use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ 4 \times \frac{22}{7} \times r^2 = 2464 \]

4. **Simplify the equation**:
Multiply \( 4 \) and \( \frac{22}{7} \):
\[ \frac{88}{7} r^2 = 2464 \]

5. **Isolate \( r^2 \)**:
To isolate \( r^2 \), multiply both sides of the equation by \( \frac{7}{88} \):
\[ r^2 = 2464 \times \frac{7}{88} \]

6. **Calculate \( r^2 \)**:
First, calculate \( 2464 \div 88 \):
\[ 2464 \div 88 = 28 \]
Now multiply by \( 7 \):
\[ r^2 = 28 \times 7 = 196 \]

7. **Find \( r \)**:
To find \( r \), take the square root of \( r^2 \):
\[ r = \sqrt{196} = 14 \, \text{cm} \]

### Final Answer:
The radius of the sphere is \( 14 \, \text{cm} \).