A chord of a circle of radius 15cm subtends an angle of 60∘ at the centre. Find the areas of the corresponding minor and major segments of the circle.(Use π=3.14 and 3=1.73)

Question

A chord of a circle of radius 15cm subtends an angle of 60∘ at the centre. Find the areas of the corresponding minor and major segments of the circle.(Use π=3.14 and 3​=1.73)

Filo · Accepted Answer

In the mentioned figure,O is the centre of circle,AB is a chordAXB is a major arc,OA=OB= radius = 15 cmArc AXB subtends an angle 60o at O.Area of sector AOB=36060​× π×r2                                    =36060​×3.14×(15)2                                    =117.75cm2Area of minor segment (Area of Shaded region) = Area of sector AOB− Area of △ AOBBy trigonometry,AC=15sin30OC=15cos30And, AB=2AC∴ AB=2×15sin30=15 cm∴ OC=15cos30=1523​​=15×21.73​=12.975 cm∴ Area of △AOB=0.5×15×12.975=97.3125cm2∴ Area of minor segment (Area of Shaded region) =117.75−97.3125=20.4375 cm2Area of major segment = Area of circle − Area of minor segment                                       =(3.14×15×15)−20.4375                                        =686.0625cm2

Question Text	A chord of a circle of radius $15 c m$ subtends an angle of $6 0^{\circ}$ at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use $π = 3.14$ and $3 = 1.73$ )
Answer Type	Text solution:1
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A chord of a circle of radius $15 c m$ subtends an angle of $6 0^{\circ}$ at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use $π = 3.14$ and $3 = 1.73$ )

Text solutionVerified

Practice questions from similar books

A chord of a circle of radius 15cm subtends an angle of 60∘ at the centre. Find the areas of the corresponding minor and major segments of the circle.(Use π=3.14 and 3​=1.73)

Text solutionVerified

Practice questions from similar books

A chord of a circle of radius $15 c m$ subtends an angle of $6 0^{\circ}$ at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use $π = 3.14$ and $3 = 1.73$ )