The internal and external diameters of a hollow hemispherical vessel are 21 cm and 28 cm respectively. Find :
internal curved surface area,

Answer

To find the internal curved surface area of a hollow hemispherical vessel with given internal and external diameters, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Internal diameter (d) = 21 cm
- External diameter (D) = 28 cm

2. **Calculate the Internal Radius:**
- The radius (r) is half of the diameter.
- Internal radius (r) = d / 2 = 21 cm / 2 = 10.5 cm

3. **Formula for Curved Surface Area of a Hemisphere:**
- The formula for the curved surface area (CSA) of a hemisphere is given by:
\[ \text{Curved Surface Area} = 2\pi r^2 \]

4. **Substitute the Internal Radius into the Formula:**
- Substitute r = 10.5 cm into the formula:
\[ \text{Curved Surface Area} = 2\pi (10.5)^2 \]

5. **Calculate (10.5)^2:**
- \((10.5)^2 = 110.25\)

6. **Substitute the Value of \(\pi\):**
- Use \(\pi \approx \frac{22}{7}\):
\[ \text{Curved Surface Area} = 2 \times \frac{22}{7} \times 110.25 \]

7. **Calculate the Curved Surface Area:**
- First calculate \(2 \times \frac{22}{7} = \frac{44}{7}\):
\[ \text{Curved Surface Area} = \frac{44}{7} \times 110.25 \]
- Now, calculate \(44 \times 110.25 = 4851\):
\[ \text{Curved Surface Area} = \frac{4851}{7} \approx 693 \]

8. **Final Result:**
- The internal curved surface area of the hollow hemispherical vessel is approximately \(693 \, \text{cm}^2\).