Question

In a circle of radius $7$ cm, arc $AB$ makes one angle ${90}^{\circ }$ at the centre O. Find the length of the major arc $AB$.

• A. $28$ cm
• B. $31$ cm
• C. $33$ cm
• D. $35$ cm

Answer 1

Answer: (C)

$33$ cm

Length of an arc subtending an angle $\theta =\frac{\theta }{360}\times 2\pi R$, where R is the radius of the circle.
Here, the major arc will be the arc corresponding the bigger angle ${360}^o-{90}^o={270}^0$
So, required length of arc $AB==\frac{270}{360}\times 2\times \frac{22}{7}\times 7=33cm$