Question

If the angle of a sector is 30° and the radius of the sector is 21 cm, then length of the arc of the sector is__
(b) 11 cm
(a) 9 cm
(c) 10 cm
(d) 13 cm
​

Answer 1

${\Large{\boxed{\red{\sf{Correct = (b) \: \: 11 cm}}}}}$

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Given :-

• Angle of the sector = 30°
• Radius of the Sector = 21 cm

To find :-

• Length of the arc of the sector

Basic Concept related to Question :-

• Sector :- It is a portion of circle which is enclosed by two radius and one arc.
• Two radius of the circle are always equal to each other. Sector has two radius which of them both are equal. So, Length of the Radius is 21 cm.
• Arc of a circle is any portion of the circumference of a circle and it can be found by below given formula.

Solution :-

Length of an arc of a sector is given by :-

${\boxed{\sf{Length = \bigg( \frac{ \theta}{360 \degree} \bigg) \times2 \pi r}}}$

Here

• θ = Theta = Angle given
• π = pi = 22/7 or 3.14
• r = Radius

Substituting the values given :-

${ \implies{\sf{Length = \bigg( \cfrac{ 30 \degree}{360 \degree} \bigg) \times2 \times \cfrac{22}{7} \times 21}}}$

${ \implies{\sf{Length = \bigg( \cfrac{ 3}{36 } \bigg) \times2 \times 22 \times 3}}}$

${ \implies{\sf{Length = \bigg( \cfrac{3}{12} \bigg) \times2 \times 22 }}}$

${ \implies{\sf{Length = \bigg( \cfrac{3}{6} \bigg) \times 22 }}}$

${ \implies{\sf{Length = \bigg( \cfrac{1}{2} \bigg) \times 22 }}}$

${ \implies{\sf{Length = \cfrac{22}{2} }}}$

$\large{ \boxed{ \red{ \implies{\sf{Length = 11 \: cm}}}}}$

So Length of the arc is 11 cm.

Answer 2

$\huge \sf{ \underline{ANSWER}}$

$\huge \sf{ \underline{ \underline{Given :- }}}$

Angle of the sector = 30°

Radius of the Sector = 21 cm

$\huge \sf{ \underline{ \underline{To \: find :- }}}$

Length of the arc of the sector

$\huge{\sf{ \underline{ \underline{Solution :-}}}}$

Length of an arc of a sector is given by :-

${\sf{Length = \bigg( \frac{ \theta}{360 \degree} \bigg) \times2 \pi r}}$

Here

$\sf \: θ = Theta = Angle \: given$

$\sf \: π = pi = \frac{22}{7} \: or \: 3.14$

$\sf \: r = Radius$

Substituting the values given :-

${ = {\sf{Length = \bigg( \cfrac{ 30 \degree}{360 \degree} \bigg) \times2 \times \cfrac{22}{7} \times 21}}}$

$= {\sf{Length = \bigg( \cfrac{ 3}{36 } \bigg) \times2 \times 22 \times 3}}$

$= {\sf{Length = \bigg( \cfrac{3}{12} \bigg) \times2 \times 22 }}$

${\sf{Length = \bigg( \cfrac{3}{6} \bigg) \times 22 }}$

${\sf{Length = \bigg( \cfrac{1}{2} \bigg) \times 22 }}$

${\sf{Length = \cfrac{22}{2} }}$

$\large{ \boxed{{ \implies{\sf{Length = 11 \: cm}}}}}$

So Length of the arc is 11 cm.