How do you calculate the arc length of a circle with radius 9 cm and angle 90°?

The arc length of a circle with radius 9 cm and angle 90° is 14.14 cm.

To calculate the arc length of a circle, you can use the formula:
\[ \text{Arc Length} = \theta \times r \]
where \(\theta\) is the angle in radians and \(r\) is the radius of the circle. However, in this case, the angle is given in degrees, so we need to convert it to radians first. The conversion factor from degrees to radians is \(\frac{\pi}{180}\).

Given that the angle is 90°, we convert it to radians:
\[ 90° \times \frac{\pi}{180} = \frac{\pi}{2} \text{ radians} \]

Now, we can use the arc length formula with \(\theta = \frac{\pi}{2}\) and \(r = 9 \text{ cm}\):
\[ \text{Arc Length} = \frac{\pi}{2} \times 9 \]

Simplifying this, we get:
\[ \text{Arc Length} = \frac{9\pi}{2} \]

To find the numerical value, we approximate \(\pi\) as 3.14:
\[ \text{Arc Length} \approx \frac{9 \times 3.14}{2} = \frac{28.26}{2} = 14.13 \text{ cm} \]

Rounding to two decimal places, the arc length is approximately 14.14 cm. This method ensures you accurately calculate the arc length using the given radius and angle.