The maximum stress that can be applied to the material of a wire used to suspend an elevator is `(3)/(pi)xx10^(8)N//m^(2)` if the mass of elevator is 900 kg and it move up with an acceleration `2.2m//s^(2)` than calculate the minimum radius of the wire.

Answer

To solve the problem, we need to calculate the minimum radius of the wire used to suspend an elevator based on the given maximum stress and the forces acting on the elevator.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Maximum stress (σ) = \( \frac{3}{\pi} \times 10^8 \, \text{N/m}^2 \)
- Mass of the elevator (m) = 900 kg
- Acceleration (a) = 2.2 m/s²
- Acceleration due to gravity (g) = 9.8 m/s² (standard value)

2. **Calculate the Tension in the Wire:**
The tension (T) in the wire when the elevator is moving upwards can be calculated using the formula:
\[ T = mg + ma \]
where:
- \( mg \) is the weight of the elevator,
- \( ma \) is the additional force due to acceleration.

Substituting the values:
\[ T = 900 \times 9.8 + 900 \times 2.2 \]
\[ T = 8820 + 1980 = 10800 \, \text{N} \]

3. **Relate Tension to Stress:**
The stress (σ) in the wire is given by the formula:
\[ \sigma = \frac{T}{A} \]
where \( A \) is the cross-sectional area of the wire. For a circular wire, the area \( A \) can be expressed as:
\[ A = \pi r^2 \]
Thus, we can rewrite the stress equation as:
\[ \sigma = \frac{T}{\pi r^2} \]

4. **Substituting Known Values:**
We know the maximum stress and the tension, so we can set up the equation:
\[ \frac{3}{\pi} \times 10^8 = \frac{10800}{\pi r^2} \]

5. **Eliminate π from the Equation:**
Multiplying both sides by \( \pi r^2 \) gives:
\[ 3 \times 10^8 r^2 = 10800 \]
Dividing both sides by \( 3 \times 10^8 \):
\[ r^2 = \frac{10800}{3 \times 10^8} \]

6. **Calculate \( r^2 \):**
\[ r^2 = \frac{10800}{3 \times 10^8} = \frac{10800}{3} \times 10^{-8} = 3600 \times 10^{-8} = 3.6 \times 10^{-5} \, \text{m}^2 \]

7. **Calculate the Radius \( r \):**
Taking the square root of both sides:
\[ r = \sqrt{3.6 \times 10^{-5}} = 6 \times 10^{-3} \, \text{m} = 6 \, \text{mm} \]

### Final Answer:
The minimum radius of the wire is \( 6 \, \text{mm} \).