Find the surface area of a sphere of radius :
(i) 10.5 cm (ii) 5.6 cm (iii) 14 cm

Answer

To find the surface area of a sphere, we use the formula:

\[ \text{Surface Area} = 4 \pi r^2 \]

where \( r \) is the radius of the sphere.

Let's calculate the surface area for each given radius step by step.

### Part (i): Radius = 10.5 cm

1. **Identify the radius**:
\[ r = 10.5 \, \text{cm} \]

2. **Substitute the radius into the formula**:
\[ \text{Surface Area} = 4 \pi (10.5)^2 \]

3. **Calculate \( (10.5)^2 \)**:
\[ (10.5)^2 = 110.25 \]

4. **Substitute \( (10.5)^2 \) back into the formula**:
\[ \text{Surface Area} = 4 \pi \times 110.25 \]

5. **Use \( \pi \approx \frac{22}{7} \)**:
\[ \text{Surface Area} = 4 \times \frac{22}{7} \times 110.25 \]

6. **Calculate \( 4 \times \frac{22}{7} \)**:
\[ 4 \times \frac{22}{7} = \frac{88}{7} \]

7. **Now calculate the surface area**:
\[ \text{Surface Area} = \frac{88}{7} \times 110.25 \]
\[ \text{Surface Area} \approx 3539.14 \, \text{cm}^2 \]

### Part (ii): Radius = 5.6 cm

1. **Identify the radius**:
\[ r = 5.6 \, \text{cm} \]

2. **Substitute the radius into the formula**:
\[ \text{Surface Area} = 4 \pi (5.6)^2 \]

3. **Calculate \( (5.6)^2 \)**:
\[ (5.6)^2 = 31.36 \]

4. **Substitute \( (5.6)^2 \) back into the formula**:
\[ \text{Surface Area} = 4 \pi \times 31.36 \]

5. **Use \( \pi \approx \frac{22}{7} \)**:
\[ \text{Surface Area} = 4 \times \frac{22}{7} \times 31.36 \]

6. **Calculate \( 4 \times \frac{22}{7} \)**:
\[ 4 \times \frac{22}{7} = \frac{88}{7} \]

7. **Now calculate the surface area**:
\[ \text{Surface Area} = \frac{88}{7} \times 31.36 \]
\[ \text{Surface Area} \approx 394.24 \, \text{cm}^2 \]

### Part (iii): Radius = 14 cm

1. **Identify the radius**:
\[ r = 14 \, \text{cm} \]

2. **Substitute the radius into the formula**:
\[ \text{Surface Area} = 4 \pi (14)^2 \]

3. **Calculate \( (14)^2 \)**:
\[ (14)^2 = 196 \]

4. **Substitute \( (14)^2 \) back into the formula**:
\[ \text{Surface Area} = 4 \pi \times 196 \]

5. **Use \( \pi \approx \frac{22}{7} \)**:
\[ \text{Surface Area} = 4 \times \frac{22}{7} \times 196 \]

6. **Calculate \( 4 \times \frac{22}{7} \)**:
\[ 4 \times \frac{22}{7} = \frac{88}{7} \]

7. **Now calculate the surface area**:
\[ \text{Surface Area} = \frac{88}{7} \times 196 \]
\[ \text{Surface Area} \approx 2464 \, \text{cm}^2 \]

### Summary of Results:
- (i) Surface Area for radius 10.5 cm: **Approx. 3539.14 cm²**
- (ii) Surface Area for radius 5.6 cm: **Approx. 394.24 cm²**
- (iii) Surface Area for radius 14 cm: **Approx. 2464 cm²**