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A chord of a circle of radius 10 cm subtends a right angle at

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A chord of a circle of radius $10 c m$ subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use $π = 3.14$ )

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A chord of a circle of radius

10 c m

subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use

π = 3.14

)

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

(i) Area of minor segment (shaded region)

=

Area of the quadrant

A OB -

Area of the

△ A OB

= \frac{1}{4} \times π r^{2} - \frac{1}{2} \times A O \times OB

= \frac{1}{4} \times 3.14 \times (10 c m)^{2} - \frac{1}{2} \times 10 c m \times 10 c m

= \frac{1}{4} \times 3.14 \times 100 c m^{2} - 50 c m^{2}

= 78.5 c m^{2} - 50 c m^{2}

= 28.5 c m^{2}

(ii) Area of the major segment

=

Area of the circle

-

Area of the minor segment

= π r^{2} - 28.5 c m^{2}

= 3.14 \times (10 c m)^{2} - 28.5 c m^{2}

= 314 c m^{2} - 28.5 c m^{2}

= 285.5 c m^{2}

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Question Text	A chord of a circle of radius $10 c m$ subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use $π = 3.14$ )
Answer Type	Text solution:1
Upvotes	150