The rain water from a roof af dimensions ` 22 m xx 20 m ` drains into a cylindrical vessel having diameter of bases 2 m and height 3.5 m. If the rain water collected form the roof just fill the cylindrica vessl, them find the rainfull (in cm).

Explanation

To solve the problem, we need to find the amount of rainfall in centimeters based on the given dimensions of the roof and the cylindrical vessel. Here’s a step-by-step solution:

### Step 1: Calculate the Volume of the Cylindrical Vessel
The formula for the volume \( V \) of a cylinder is given by:

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

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

Given:
- Diameter of the base = 2 m, so the radius \( r = \frac{2}{2} = 1 \) m.
- Height \( h = 3.5 \) m.

Now, substituting the values into the formula:

\[ V = \pi \times (1)^2 \times 3.5 = \pi \times 1 \times 3.5 = 3.5\pi \, \text{m}^3 \]

Using \( \pi \approx \frac{22}{7} \):

\[ V = \frac{22}{7} \times 3.5 = \frac{22 \times 35}{7 \times 10} = \frac{770}{70} = 11 \, \text{m}^3 \]

### Step 2: Calculate the Volume of Rainwater Collected from the Roof
The volume of rainwater collected from the roof can be calculated using the formula for the volume of a cuboid:

\[ V = \text{length} \times \text{width} \times \text{height} \]

Given:
- Length = 22 m,
- Width = 20 m,
- Height = \( h \) (which we will denote as \( x \) in meters).

Thus, the volume of rainwater is:

\[ V = 22 \times 20 \times x = 440x \, \text{m}^3 \]

### Step 3: Set the Volume of Rainwater Equal to the Volume of the Cylindrical Vessel
Since the rainwater collected fills the cylindrical vessel completely, we can set the two volumes equal to each other:

\[ 440x = 11 \]

### Step 4: Solve for \( x \)
Now, solving for \( x \):

\[ x = \frac{11}{440} = \frac{1}{40} \, \text{m} \]

### Step 5: Convert \( x \) from Meters to Centimeters
To convert meters to centimeters, we multiply by 100:

\[ x = \frac{1}{40} \times 100 = 2.5 \, \text{cm} \]

### Final Answer
The rainfall is **2.5 cm**.

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