Question

find the radius of a circle in which a central angle of 72° intercepts an arc of length 22cm? ​

Answer 1

$\huge{\mathfrak{\underline{Answer:-}}}$

$\large{\bf{17.5cm}}$

$\huge{\mathfrak{\underline{Explanation:-}}}$

Given :-

Arc = 22cm

Angle (Φ) = 72°

$\rule{200}{2}$

To find :-

Radius

$\rule{200}{2}$

Solution :-

Use formula

$\huge{\bf{\boxed{\boxed{{\Theta} \: = {\frac{L}{R}}}}}}$

Convert Φ in radians = 72 × π/180

» 2π /5

2π/5 = 22/R

R = 5×7/2

R = 35/2

R = 17.5 cm

Radius is of 17.5 cm

Answer 2

Given,

$\mathrm{l=22cm}\\\\\mathrm{\theta=72\textdegree=\left(\dfrac{2\times180}{5}\right)^{\circ}\ =\ \left(\dfrac{2\pi}{5}\right)^c}$

We have,

$\mathrm{r\ =\ \dfrac{l}{\theta}\ =\ \dfrac{22}{\left(\dfrac{2\pi}{5}\right)}\ =\ \dfrac{22\times 5}{2\pi}\ cm}$

Taking  $\pi=\dfrac{22}{7},$

$\mathrm{r\ =\ \dfrac{22\times5}{2\times\dfrac{22}{7}}\ =\ \dfrac{22\times 5\times 7}{2\times 22}\ =}\ \mathbf{17.5\ cm}$