Assertion (A): A chord of a circle of radius 14 cm makes a right angle at the centre. The area of the minor segment is 56 cm². Reason (R): Angle described by the

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Solution

Q.
Assertion (A): A chord of a circle of radius 14 cm makes a right angle at the centre. The area of the minor segment is $56 c m ² .$

Reason (R): Angle described by the minute hand in 5 minutes = $6 °$

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)

3 Assertion (A) is true but Reason (R) is false.

4 Assertion (A) is false but Reason (R) is true.

Ans.
(3)

Area of minor segmen

t $= Area of sector - Area of ∆ O A B = \frac{90 °}{360 °} \times π \times (14)^{2} - \frac{1}{2} \times 14 \times 14$

$= \frac{1}{4} \times \frac{22}{7} \times 14 \times 14 - 7 \times 14 = 154 - 98 = 56 {cm}^{2} ∴ A s s e r t i o n (A) i s t r u e .$

$A n g l e d e s c r i b e d b y t h e m i n u t e h a n d i n 5 m i n u t e s = 5 \times 6 ° = 30 ° S o R e a s o n (R) i s f a l s e .$

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