Question

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

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

Answer 1

Answer: (B)

Given radius, $r = 100\,cm$ and arc length, $I = 22 \,cm$
We know that, $l = r\theta$
$\theta=\frac{l}{r}=\frac{\text{Arc length}}{\text{Radius}}=\frac{22}{100}$
$=0.22 \,rad$
$=0.22\times\frac{180}{\pi}$ degree $=0.22\times\frac{180 \times 7}{22}$
$=\frac{126^{\circ}}{10}=12 \frac{6^{\circ}}{10}$
$=12^{\circ}+\frac{6}{10}\times60'\,\left[\because 1^{\circ}=60'\right]$
$=12^{\circ}+36'=12^{\circ}\,36'$
Hence, the degree measure of the required angle is $12^{\circ}36'$.