How many cubic metres of earth must be dug out to sink a well 14 m deep and having a radius of 4 m. If the earth taken out is spread over a plot of dimension `(25 m xx 16 m)`. What is the height of the plateform so formed?

Answer

To solve the problem step by step, we will calculate the volume of the well (which is in the shape of a cylinder) and then find the height of the platform formed when this volume of earth is spread over a rectangular plot.

### Step 1: Calculate the Volume of the Well
The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (depth of the well),
- \( \pi \) is approximately \( \frac{22}{7} \).

Given:
- Radius \( r = 4 \) m
- Height \( h = 14 \) m

Substituting the values into the formula:
\[ V = \frac{22}{7} \times (4^2) \times 14 \]
Calculating \( 4^2 \):
\[ 4^2 = 16 \]
Now substituting back:
\[ V = \frac{22}{7} \times 16 \times 14 \]

Calculating \( 16 \times 14 \):
\[ 16 \times 14 = 224 \]
Now substituting:
\[ V = \frac{22}{7} \times 224 \]

Calculating \( \frac{224}{7} \):
\[ 224 \div 7 = 32 \]
Now substituting:
\[ V = 22 \times 32 = 704 \, \text{cubic meters} \]

### Step 2: Calculate the Volume of the Platform
The volume of the earth dug out will be equal to the volume of the platform formed when this earth is spread over a rectangular plot. The volume \( V_p \) of the platform can be calculated using the formula:
\[ V_p = \text{length} \times \text{breadth} \times \text{height} \]

Given:
- Length = 25 m
- Breadth = 16 m
- Let the height be \( h_p \).

Thus, the volume of the platform is:
\[ V_p = 25 \times 16 \times h_p \]

### Step 3: Set the Volumes Equal
Since the volume of the dug-out earth is equal to the volume of the platform:
\[ 704 = 25 \times 16 \times h_p \]

Calculating \( 25 \times 16 \):
\[ 25 \times 16 = 400 \]
Now substituting:
\[ 704 = 400 \times h_p \]

### Step 4: Solve for Height of the Platform
To find \( h_p \):
\[ h_p = \frac{704}{400} \]
Calculating:
\[ h_p = 1.76 \, \text{meters} \]

### Final Answer
The height of the platform formed is **1.76 meters**.

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