Find the total surface area of the hemisphere whose radius is :
(a) 14 cm
(b) 5 cm

Answer

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

\[ \text{Total Surface Area (TSA)} = 3\pi r^2 \]

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

### Step-by-Step Solution:

#### (a) For radius \( r = 14 \) cm:

1. **Substitute the radius into the formula**:
\[ \text{TSA} = 3\pi (14)^2 \]

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

3. **Substitute \( 196 \) back into the formula**:
\[ \text{TSA} = 3\pi \times 196 \]

4. **Calculate \( 3 \times 196 \)**:
\[ 3 \times 196 = 588 \]

5. **Thus, the TSA becomes**:
\[ \text{TSA} = 588\pi \text{ cm}^2 \]

6. **Using \( \pi \approx \frac{22}{7} \)**, convert to numerical value:
\[ \text{TSA} = 588 \times \frac{22}{7} \]

7. **Calculate**:
\[ 588 \div 7 = 84 \]
\[ 84 \times 22 = 1848 \]

8. **Final answer for radius 14 cm**:
\[ \text{TSA} = 1848 \text{ cm}^2 \]

#### (b) For radius \( r = 5 \) cm:

1. **Substitute the radius into the formula**:
\[ \text{TSA} = 3\pi (5)^2 \]

2. **Calculate \( (5)^2 \)**:
\[ (5)^2 = 25 \]

3. **Substitute \( 25 \) back into the formula**:
\[ \text{TSA} = 3\pi \times 25 \]

4. **Calculate \( 3 \times 25 \)**:
\[ 3 \times 25 = 75 \]

5. **Thus, the TSA becomes**:
\[ \text{TSA} = 75\pi \text{ cm}^2 \]

6. **Using \( \pi \approx \frac{22}{7} \)**, convert to numerical value:
\[ \text{TSA} = 75 \times \frac{22}{7} \]

7. **Calculate**:
\[ 75 \times 22 = 1650 \]
\[ 1650 \div 7 \approx 235.714 \]

8. **Final answer for radius 5 cm**:
\[ \text{TSA} \approx 235.714 \text{ cm}^2 \]

### Summary of Answers:
- (a) Total Surface Area for radius 14 cm: \( 1848 \text{ cm}^2 \)
- (b) Total Surface Area for radius 5 cm: \( 235.714 \text{ cm}^2 \)