Question

3.3 A circle has a radius of 12cm. An angle of 3.2 radians is subtended at the centre by an arc. Calculate the length of the arc. (3)​

Answer 1

S = 38.4 centimeters.

Explanation:

Given the following data;

• Radius, r = 12 cm
• Angle = 3.2 rads

To find the length of the arc of a circle;

A full circle measures an angle of 360 degrees.

π = 180°

So; Angle, A = 360° = 2π

Therefore, a full circle is equal to 2π in terms of radians (rads).

Also, the circumference (the length of an arc) of a circle is equal to 2πr or Ar.

Mathematically, the length of the arc of a circle is given by the formula;

S = rA

Where;

• S is the length of the arc.
• A is the angle measured in radians.

Substituting into the formula, we have;

S = 12 * 3.2

S = 38.4 centimeters.