Question

In a circle of radius 21 cm an arc subtends an angle 60° at the
centre, then find the area of sector.
Section - C​

Answer 1

Answer:

area of the circle is 539 cm^2

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: QuEsTiOn:- \: \star}}}}}$

In a circle of radius 21 cm an arc subtends an angle 60° at the centre, then find the area of sector.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

The length of the arc is 22 cm & Area of sector of a circle is 231 cm².

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Given :-

$Radius \: of \: circle \: ,r \: = \: 21 cm \\ </p><p></p><p>Angle \: subtended \: by \: an \: arc, \: θ \: = 60° \\ </p><p></p><p>Length \: of \: the \: arc, \: l \: = \: (θ/360) \: × \: 2πr \\ </p><p></p><p>l \: = \:  (60°/360°) \: × \: 2π \: × \: 21 \\ </p><p></p><p>l \: = \: 1/6 \: × \: 2 \: × 22/7 \: × 21 \\ </p><p></p><p>l \: = \: (44 × 3)/6 \\ </p><p></p><p>l \: = \: 22 cm$

Length of the arc, l = 22 cm  

Area of the sector of a circle, A = (θ/360) × πr²

$A \: = \: (60°/360°) \: × π \: ×21² \\ </p><p></p><p>A \: = \: 1/6 \: × 22/7 \: × 21 \: × 21 \\ </p><p></p><p>A \: = \: (22 × 21× 3)/6 \\ </p><p></p><p>A \: = \: 11 \: × \: 21 \\ </p><p></p><p>A \: = \: 231 cm² \\ </p><p>$

Area of sector of a circle ,

$A \: = \: 2 31 \: cm ^{2}$

$\mathfrak{\huge{\green{\underline{\underline{Hence }}}}}$

The length of the arc is 22 cm & Area of sector of a circle is 231 cm².