Assertion (A): In a circle of radius 6 cm, the angle of a sector 60°. Then the area of the sector is 18\frac{6}{7}{\mathrm{\ cm}}^2. Reason (R): Circumference

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Solution

Q.
Assertion (A): In a circle of radius 6 cm, the angle of a sector $60 ° .$ Then the area of the sector is $18 \frac{6}{7} {cm}^{2} .$

Reason (R): Circumference of the circle with radius r is $2 π r$ .

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.
(2)

We have

$r = 6 cm and central angle θ = 60 ° ∴ A r e a o f s e c t o r = \frac{θ}{360 °} \times π r^{2} = \frac{60 °}{360 °} \times \frac{22}{7} \times (6)^{2} = \frac{1}{6} \times \frac{22}{7} \times 36 = \frac{132}{7} {cm}^{2} = 18 \frac{6}{7} {cm}^{2} A l s o, c i r c u m f e r e n c e o f t h e c i r c l e w i t h r a d i u s r i s 2 π r B o t h A s s e r t i o n (A) a n d R e a s o n (R) a r e t r u e b u t R e a s o n (R) i s n o t t h e c o r r e c t e x p l a n a t i o n o f A s s e r t i o n (A) .$

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