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) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord

(i) We know that, Length of an arc of sector of angle θ = 2πr Substituting values we get : Hence, length of arc = 22 cm. (ii) We know that, Area of sector of angle θ and radius r = Substituting values we get : Hence, area of sector = 231 cm 2 . (iii) In triangle OAB, OM ⊥ AB In triangle OAM and OMB, ∠OMA = ∠OMB = 90° OA = OB (Radius of same circle) OM = OM (Common) ∴ △OAM ≅ △OMB (By RHS axiom) ∴ ∠MOB = ∠MOA = = 30°. [By C.P.C.T.] In △MOB, ⇒ sin 30° = ⇒ ⇒ MB = = 10.5 cm By C.P.C.T. MA = MB = 10.5 cm AB = MA + MB = 21 cm. Since, OA = OB = AB. ∴ △AOB is an equilateral triangle. We know that, Area of equilateral triangle = (Side) 2 Substituting values we get : From figure, Area of segment APB = Area of sector AOBP - Area of triangle AOB = Hence, area of segment APB =

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

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A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :
(i) minor segment
(ii) major sector.
(Use π = 3.14)

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Mathematics

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) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord

Circles

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The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :
(i) minor segment
(ii) major sector.
(Use π = 3.14)

Mathematics

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) area of the sector formed by the arc(iii) area of the segment formed by the corresponding chord

Circles

Related Questions

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :(i) minor segment(ii) major sector.(Use π = 3.14)

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) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :
(i) minor segment
(ii) major sector.
(Use π = 3.14)