To find the length of arc \(AXB\) and the area of sector \(AXBO\) in circle \(O\) with a radius of 9 cm, we need to use the formulas for arc length and sector area.
1. **Length of Arc \(AXB\)**:
The formula for the length of an arc is given by:
\[ \text{Arc Length} = \frac{\text{Central Angle}}{360^\circ} \times 2\pi r \]
Since arc \(AXB\) is a semicircle, its central angle is \(180^\circ\). Substituting the values into the formula:
\[ \text{Arc Length} = \frac{180^\circ}{360^\circ} \times 2\pi \times 9 \]
\[ \text{Arc Length} = \frac{1}{2} \times 2\pi \times 9 = 9\pi \]
2. **Area of Sector \(AXBO\)**:
The formula for the area of a sector is given by:
\[ \text{Sector Area} = \frac{\text{Central Angle}}{360^\circ} \times \pi r^2 \]
Again, since sector \(AXBO\) is a semicircle, its central angle is \(180^\circ\). Substituting the values into the formula:
\[ \text{Sector Area} = \frac{180^\circ}{360^\circ} \times \pi \times 9^2 \]
\[ \text{Sector Area} = \frac{1}{2} \times \pi \times 81 = \frac{81\pi}{2} \]
Therefore:
- Length of arc \(AXB\) = \(9\pi\) cm
- Area of sector \(AXBO\) = \(\frac{81\pi}{2}\) square cm
