In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord?

Concept:

Length of arc = \(\frac{\theta }{{360}} \times 2\pi r\)

Calculation:

Given Data;

Diameter = 44 cm

\({\rm{Radius}} = {\rm{}}\frac{{{\rm{Diameter}}}}{2}{\rm{}} = {\rm{}}\frac{{44}}{2}{\rm{}} = {\rm{\;}}22{\rm{cm}}\)

Chord length = 22 cm

Figure

In triangle AOB;

OA = OB = Radius = 22 cm

AB = 22 cm

∵ All sides are equal so triangle is equilateral

∴ All angles are same, \(\theta = 60\)

\({\rm{Length\;of\;arc}} = {\rm{}}\frac{{\rm{\theta }}}{{360}} \times 2{\rm{\pi r}} = {\rm{}}\frac{{60}}{{360}} \times 2 \times \frac{{22}}{7} \times 22{\rm{}} = {\rm{}}\frac{1}{6} \times \frac{{968}}{7}{\rm{}} = {\rm{}}\frac{{484}}{{21}}{\rm{\;cm}}\)