Question

If an arc of a circle of radius 10.5 cm, subtends an angle of 60° at the centre, then find the length of the arc.

Hint:

$10.5$ is often easier to calculate as $21/2$ when working with the fraction $22/7$.

Answer 1

Step 1: Write the formula for the length of an arc.
The length of an arc of a circle is calculated using the formula:
\( \text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r \)
where \( \theta \) is the angle at the centre and \( r \) is the radius of the circle.

Step 2: Substitute the given values.
Here, the radius \( r = 10.5 \) cm and the angle \( \theta = 60^\circ \).
Substituting these values into the formula:
\( \text{Arc Length} = \frac{60}{360} \times 2\pi \times 10.5 \)

Step 3: Simplify the fraction.
\( \frac{60}{360} = \frac{1}{6} \)
So the expression becomes:
\( \text{Arc Length} = \frac{1}{6} \times 2\pi \times 10.5 \)

Step 4: Perform the multiplication.
First multiply \(2 \times 10.5 = 21\).
So the expression becomes:
\( \text{Arc Length} = \frac{1}{6} \times 21\pi \)

Step 5: Final simplification.
\( \frac{21}{6} = 3.5 \)
Thus,
\( \text{Arc Length} = 3.5\pi \) cm.

Final Answer:
The length of the arc is \( 3.5\pi \) cm, which is approximately \( 11 \) cm.