What is the arc length of a circle with radius 6 cm and angle 45°?

The arc length of a circle with radius 6 cm and angle 45° is 4.71 cm.

To find 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. First, we need to convert the angle from degrees to radians. We know that \( 180^\circ \) is equivalent to \( \pi \) radians. Therefore, \( 45^\circ \) can be converted to radians by multiplying by \( \frac{\pi}{180} \):

\[ 45^\circ \times \frac{\pi}{180} = \frac{\pi}{4} \text{ radians} \]

Now that we have the angle in radians, we can use the arc length formula. Given that the radius \( r \) is 6 cm, we substitute the values into the formula:

\[ \text{Arc Length} = \frac{\pi}{4} \times 6 \]

Simplifying this, we get:

\[ \text{Arc Length} = \frac{6\pi}{4} = \frac{3\pi}{2} \]

To get a numerical value, we approximate \( \pi \) as 3.14:

\[ \text{Arc Length} \approx \frac{3 \times 3.14}{2} = 4.71 \text{ cm} \]

So, the arc length of a circle with a radius of 6 cm and an angle of 45° is approximately 4.71 cm. This method can be used for any circle, as long as you know the radius and the angle in degrees.