Question

find the length of arc area of a sectarian of a circle makes an angel of 70°at the centre and radius of circle is 21 cm.​

Answer 1

$\huge{\boxed{\fcolorbox{cyan}{pink} {Answer}}}$

$\sf{GIVEN}$

• $\sf{\:Radius \:(r) \:of \:the \:circle = 21cm}$
• $\sf{\:Angle \:subtended \:by \:the \:given \:arc \:{θ} = 70°}$

$\sf{TO \:FIND}$

• $\sf{\:Length \:of \:an \:arc \:area = ?¿}$

The length of arc l and area A of a sector of angle θ in a circle of radius r are given by,

We know the formula ;

$\sf\boxed{\:Length \:of \:an \:arc \:of \:an \:angle = \frac{θ}{360°} × 2πr}$

$\sf{:⟹ L = \frac{70}{360°} × 2 × \frac{22}{7} × 21}$

$\sf{:⟹ L = \frac{7 \cancel{0}}{36 \cancel{0}°} × 2 × \frac{22}{\cancel{7}_{1}} × \cancel{21}^{3}}$

$\sf{:⟹ L = \frac{7}{36°} × 2 × 22 × 3}$

$\sf{:⟹ L = \frac{7}{36°} × 132}$

$\sf{:⟹ L = \frac{924}{36°}}$

$\sf{:⟹ L = 25.66cm}$

Let's find the area of the arc of angle ;)

We know the formula ;

$\sf\boxed{Area \:of \:the \:angle = \frac{θ}{360°} × πr²}$

$\sf{:⟹ A = \frac{70}{360°} × \frac{22}{7} × (21)²}$

$\sf{:⟹ A = \frac{70}{360°} × \frac{22}{7} × (21)²}$

$\sf{:⟹ A = \frac{7 \cancel{0}}{36 \cancel{0}°} × 2 × \frac{22}{\cancel{7}_{1}} × \cancel{21}^{3} × 21}$

$\sf{:⟹ A = \frac{7}{\cancel{36}^{12}°} × 2 × 22 × \cancel{3}^{1} × 21}$

$\sf{:⟹ A = \frac{7}{\cancel{12}^{6}} × \cancel{2}^{1} × 22 × 21}$

$\sf{:⟹ A = \frac{7}{6} × 22 × 21 }$

$\sf{:⟹ A = \frac{3234}{6}}$

$\sf{:⟹ A = \cancel\frac{3234}{6}}$

$\sf{:⟹ A = 539cm²}$

_______________________________________

• $\sf\boxed{Length \:of \:the \:arc \:angle = 25.66cm}$

• $\sf\boxed{Area \:of \:the \:angle = 539cm²}$

_______________________________________