Question

Find the degree measure of the angle subtended at the centre of a circle of radius $100cm$ by an arc of length $22cm$ as shown in figure. [Use $\pi =\frac{22}{7}$]

• A. $12^{\circ }30^{\prime }$
• B. $12^{\circ }36^{\prime }$
• C. $11^{\circ }36^{\prime }$
• D. $11^{\circ }12^{\prime }$

Answer 1

Answer: (B)

Given radius, $r=100cm$ and arc length, $I=22cm$
We know that, $l=r\theta$
$\theta =\frac{l}{r}=\frac{\text{Arc length}}{\text{Radius}}=\frac{22}{100}$
$=0.22rad$
$=0.22\times \frac{180}{\pi }$ degree $=0.22\times \frac{180\times 7}{22}$
$=\frac{126^{\circ }}{10}=12\frac{6^{\circ }}{10}$
$=12^{\circ }+\frac{6}{10}\times 60^{\prime }\left[\because 1^{\circ }=60^{\prime }\right]$
$=12^{\circ }+36^{\prime }=12^{\circ }36^{\prime }$
Hence, the degree measure of the required angle is $12^{\circ }36^{\prime }$.