How do you calculate the arc length of a circle with diameter 10 cm and angle 60°?

The arc length is calculated using the formula: \(\text{Arc Length} = \frac{\theta}{360} \times 2\pi r\).

To find the arc length of a circle, you need to know the radius and the angle subtended by the arc at the centre of the circle. In this case, the diameter of the circle is 10 cm, so the radius \(r\) is half of the diameter, which is \(5\) cm. The angle \(\theta\) given is \(60^\circ\).

The formula for the arc length \(L\) of a circle is:
\[ L = \frac{\theta}{360} \times 2\pi r \]

First, substitute the given values into the formula:
\[ L = \frac{60}{360} \times 2\pi \times 5 \]

Simplify the fraction \(\frac{60}{360}\):
\[ \frac{60}{360} = \frac{1}{6} \]

Now, substitute this back into the formula:
\[ L = \frac{1}{6} \times 2\pi \times 5 \]

Multiply the constants together:
\[ L = \frac{1}{6} \times 10\pi \]

\[ L = \frac{10\pi}{6} \]

Simplify the fraction:
\[ L = \frac{5\pi}{3} \]

To get a numerical value, you can approximate \(\pi\) as \(3.14\):
\[ L \approx \frac{5 \times 3.14}{3} \]

\[ L \approx \frac{15.7}{3} \]

\[ L \approx 5.23 \text{ cm} \]

So, the arc length of the circle with a diameter of 10 cm and an angle of 60° is approximately 5.23 cm.