A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread to form a platform of divisions 22 m `xx` 14 m. Find the height of the platform.

Answer

To solve the problem, we need to find the height of the platform formed by the earth dug out from the well. We will follow these steps:

### Step 1: Calculate the volume of the well
The well is in the shape of a cylinder. The formula for the volume \( V \) of a cylinder is given by:

\[ V = \pi r^2 h \]

Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

Given:
- Diameter of the well = 7 m, therefore radius \( r = \frac{7}{2} = 3.5 \) m.
- Height of the well \( h = 20 \) m.

Now, substituting the values into the formula:

\[ V = \pi (3.5)^2 (20) \]

Calculating \( (3.5)^2 \):

\[ (3.5)^2 = 12.25 \]

Now substituting back into the volume formula:

\[ V = \pi \times 12.25 \times 20 \]
\[ V = 245\pi \text{ cubic meters} \]

### Step 2: Calculate the area of the platform
The platform is rectangular in shape. The area \( A \) of a rectangle is given by:

\[ A = \text{length} \times \text{width} \]

Given:
- Length = 22 m,
- Width = 14 m.

Now substituting the values:

\[ A = 22 \times 14 \]
\[ A = 308 \text{ square meters} \]

### Step 3: Calculate the height of the platform
The volume of the earth dug out from the well is used to form the platform. The volume of the platform can also be expressed as:

\[ \text{Volume of the platform} = \text{Area of the platform} \times \text{Height of the platform} \]

Let \( h_p \) be the height of the platform. Therefore:

\[ 245\pi = 308 \times h_p \]

Now, solving for \( h_p \):

\[ h_p = \frac{245\pi}{308} \]

Using \( \pi \approx 3.14 \):

\[ h_p \approx \frac{245 \times 3.14}{308} \]
\[ h_p \approx \frac{768.3}{308} \approx 2.5 \text{ meters} \]

### Conclusion
The height of the platform is approximately 2.5 meters.

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