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 :
Height of the platform formed by spreading the earth on the rectangular plot.

Answer

To find the height of the platform formed by spreading the earth dug from the circular well on the rectangular plot, we can follow these steps:

### Step 1: Calculate the Volume of the Circular Well
The volume \( V \) of a cylinder (which is the shape of the well) can be calculated using the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the well,
- \( h \) is the depth of the well.

Given:
- Radius \( r = 3.5 \, \text{m} \)
- Depth \( h = 20 \, \text{m} \)

Substituting the values:
\[ V = \pi \times (3.5)^2 \times 20 \]

### Step 2: Calculate \( (3.5)^2 \)
\[ (3.5)^2 = 12.25 \]

### Step 3: Substitute and Calculate the Volume
Now substituting \( (3.5)^2 \) into the volume formula:
\[ V = \pi \times 12.25 \times 20 \]
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 12.25 \times 20 \]

### Step 4: Simplify the Calculation
First, calculate \( 12.25 \times 20 \):
\[ 12.25 \times 20 = 245 \]
Now substituting back:
\[ V = \frac{22}{7} \times 245 \]

### Step 5: Calculate \( \frac{22 \times 245}{7} \)
Calculating \( 22 \times 245 \):
\[ 22 \times 245 = 5390 \]
Now divide by 7:
\[ V = \frac{5390}{7} = 770 \, \text{m}^3 \]

### Step 6: Calculate the Volume of the Rectangular Plot
The volume \( V' \) of the rectangular plot can be calculated using the formula:
\[ V' = \text{Length} \times \text{Breadth} \times \text{Height} \]
Let the height of the platform be \( H \). Given:
- Length = 14 m
- Breadth = 11 m

So,
\[ V' = 14 \times 11 \times H \]

### Step 7: Set the Volumes Equal
Since the volume of the soil dug is equal to the volume of the platform formed:
\[ 770 = 14 \times 11 \times H \]

### Step 8: Calculate \( 14 \times 11 \)
Calculating \( 14 \times 11 \):
\[ 14 \times 11 = 154 \]

### Step 9: Substitute and Solve for \( H \)
Now substituting back:
\[ 770 = 154 \times H \]
To find \( H \):
\[ H = \frac{770}{154} \]

### Step 10: Simplify the Division
Calculating \( \frac{770}{154} \):
\[ H = 5 \, \text{m} \]

### Final Answer
The height of the platform formed by spreading the earth on the rectangular plot is \( 5 \, \text{m} \).

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