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In a circle of radius 21 cm ,an arc subtends an angle of {60}^

Question

In a circle of radius $21 c m$ ,an arc subtends an angle of $60^{\circ}$ at the centre.Find
$(i)$ the length of the arc
$(ii)$ the area of the sector
$(iii)$ the area of the minor segment and
$(i v)$ the area of the major segment.

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In a circle of radius

21 c m

,an arc subtends an angle of

60^{\circ}

at the centre.Find

(i)

the length of the arc

(ii)

the area of the sector

(iii)

the area of the minor segment and

(i v)

the area of the major segment.

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Text solutionVerified

θ = 6 0^{o}

r = 21 c m

(i) Length of arc

= \frac{60}{360} \times 2 π \times 21

= \frac{1}{6} \times 2 \times \frac{22}{7} \times 21 = 22 c m

(ii) Area of sector

= \frac{60}{360} \times π \times (21)^{2}

= \frac{1}{6} \times \frac{22}{7} \times (21)^{2} = 231 c m^{2}

(iii) Minor segment

Area of

Δ A OB = \frac{1}{2} \times r^{2} \times sin θ = \frac{1}{2} \times (21)^{2} \times sin 60

= \frac{1}{2} \times 21 \times 21 \times \frac{3}{2} = 190.95 c m^{2}

Area of circle

= π r^{2} = \frac{22}{7} \times (21)^{2} = 1386 c m^{2}

Area of minor segment ABC

=

Area of circle

-

Area of

Δ

AOB

= 1386 - 190.95

= 1195.05 c m^{2}

(iv) Area of major segment

=

Area of circle - Area of minor segment

= 1386 - 1195.05

= 190.95 c m^{2}

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Question Text	In a circle of radius $21 c m$ ,an arc subtends an angle of $60^{\circ}$ at the centre.Find $(i)$ the length of the arc $(ii)$ the area of the sector $(iii)$ the area of the minor segment and $(i v)$ the area of the major segment.
Answer Type	Text solution:1
Upvotes	150

In a circle of radius 21 cm ,an arc subtends an angle of 60∘ at the centre.Find (i) the length of the arc(ii) the area of the sector(iii) the area of the minor segment and (iv) the area of the major segment.

Text solutionVerified

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In a circle of radius $21 c m$ ,an arc subtends an angle of $60^{\circ}$ at the centre.Find
$(i)$ the length of the arc
$(ii)$ the area of the sector
$(iii)$ the area of the minor segment and
$(i v)$ the area of the major segment.