A 15 m deep well with radius 2.8 m is dug and the earth taken out from it is spread evenly to form a platform of breadth 8 m and height 1.5 m. What will be the length of the platform? 2.8 मीटर त्रिज्या वाला, एक 15 मीटर गहरा कुआं खोदा जाता है और इससे निकली मिट्टी को बराबर करके 8 मीटर चौड़ा और 1.5 मीटर ऊंचा एक चबूतरा बनाया जाता है। इसे चबूतरे की लंबाई क्या है? `(pi = 22/7)`

Options

A. 28.8 m
B. 30.8 m
C. 28.4 m
D. 30.2 m

Answer

To solve the problem, we need to find the length of the platform formed by the earth taken out from the well. We will use the concept of volume for both the cylindrical well and the cuboidal platform.

### Step-by-Step Solution:

1. **Calculate the volume of the cylindrical well:**
The formula for the volume of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

Given:
- Radius \( r = 2.8 \) m
- Height \( h = 15 \) m
- Using \( \pi = \frac{22}{7} \)

Substitute the values into the formula:
\[ V = \frac{22}{7} \times (2.8)^2 \times 15 \]

2. **Calculate \( (2.8)^2 \):**
\[ (2.8)^2 = 7.84 \]

3. **Substitute back to find the volume:**
\[ V = \frac{22}{7} \times 7.84 \times 15 \]

4. **Calculate \( \frac{22}{7} \times 7.84 \):**
\[ \frac{22 \times 7.84}{7} = 22 \times 1.12 = 24.64 \]

5. **Now calculate the volume:**
\[ V = 24.64 \times 15 = 369.6 \text{ m}^3 \]

6. **Calculate the volume of the cuboidal platform:**
The formula for the volume of a cuboid is given by:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Breadth = 8 m
- Height = 1.5 m
- Let the length be \( L \).

Thus, we have:
\[ 369.6 = L \times 8 \times 1.5 \]

7. **Calculate \( 8 \times 1.5 \):**
\[ 8 \times 1.5 = 12 \]

8. **Substitute back to find the length:**
\[ 369.6 = L \times 12 \]

9. **Solve for \( L \):**
\[ L = \frac{369.6}{12} = 30.8 \text{ m} \]

### Final Answer:
The length of the platform is \( 30.8 \) meters.