| Assertion (A): A sector is cut from a circle of radius\[\text{42 cm}\]. The central angle of the sector is \[150{}^\circ \]. The perimeter of the sector is\[\text{194 cm}\] |
| Reason (R): \[\text{Perimeter of sector}=2\,(radius)+\] \[\text{Length of corresponding arc of sector}\] |
A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
C) Assertion (A) is true but Reason (R) is false
D) Assertion (A) is false but Reason (R) is true
Correct Answer: A
Solution :
| [a] We have, radius of circle, \[r=42\,cm\] |
| Sector angle, \[\theta =150{}^\circ \] |
| \[\therefore \] Perimeter of sector \[=2r+\frac{\theta }{360{}^\circ }\times 2\pi r\] |
| \[=2\times 42+\frac{150{}^\circ }{360{}^\circ }\times 2\times \frac{22}{7}\times 42\] |
| \[=84+110=194cm\] |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of Assertion. |
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