A circular well of radius 3.5 m is dug 20 m deep and the earth so dug is spread on a rectangular plot of length 14 m and breadth 11 m. Find :
Volume of the earth dug-out.

Answer

To solve the problem, we need to find the volume of the earth dug out from the circular well and then confirm that this volume can be spread over the rectangular plot.

### Step-by-Step Solution:

1. **Identify the dimensions of the well:**
- Radius (r) = 3.5 m
- Depth (h) = 20 m

2. **Calculate the volume of the circular well:**
The volume \( V \) of a cylinder (which is the shape of the well) is given by the formula:
\[ V = \pi r^2 h \]
Here, we will use \( \pi \approx \frac{22}{7} \).

3. **Substituting the values into the formula:**
\[ V = \frac{22}{7} \times (3.5)^2 \times 20 \]

4. **Calculate \( (3.5)^2 \):**
\[ (3.5)^2 = 12.25 \]

5. **Now substitute \( (3.5)^2 \) back into the volume formula:**
\[ V = \frac{22}{7} \times 12.25 \times 20 \]

6. **Multiply \( 12.25 \) by \( 20 \):**
\[ 12.25 \times 20 = 245 \]

7. **Now calculate the volume:**
\[ V = \frac{22}{7} \times 245 \]

8. **Calculate \( \frac{22 \times 245}{7} \):**
- First, calculate \( 22 \times 245 = 5390 \).
- Now divide by \( 7 \):
\[ V = \frac{5390}{7} = 770 \text{ m}^3 \]

9. **The volume of earth dug out is 770 m³.**

10. **Now, we need to find the height of the soil when spread over the rectangular plot:**
- Length of the plot (L) = 14 m
- Breadth of the plot (B) = 11 m

11. **Calculate the area of the rectangular plot:**
\[ \text{Area} = L \times B = 14 \times 11 = 154 \text{ m}^2 \]

12. **Let the height of the soil spread be \( h \). The volume of the soil spread is given by:**
\[ \text{Volume} = \text{Area} \times \text{Height} = 154 \times h \]

13. **Setting the volume of the soil equal to the volume of the well:**
\[ 154h = 770 \]

14. **Now solve for \( h \):**
\[ h = \frac{770}{154} = 5 \text{ m} \]

### Final Answer:
The height of the soil when spread over the rectangular plot is **5 meters**.