| Assertion (A): The area of the quadrant of a circle having circumference of \[44cm\]is \[\frac{77}{2}c{{m}^{2}}\]. |
| Reason (R): The area of a sector of a circle of radius r with central angle x is \[\frac{x}{360{}^\circ }\times \pi {{r}^{2}}\]. |
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] Let r cm be the radius of the circle. |
| Given, circumference of circle \[=\text{44 cm}\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,2\pi r=44\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,2\times \frac{22}{7}\times r=44\Rightarrow r=7\] |
| \[\therefore \] Area of the quadrant |
| \[=\frac{1}{4}\pi {{r}^{2}}=\left( \frac{1}{4}\times \frac{22}{7}\times 7\times 7 \right)c{{m}^{2}}\] |
| \[=\frac{77}{2}c{{m}^{2}}\] |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of Assertion. |
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