| Assertion (A): If the circumference of two circles are in the ratio \[2:e\] then ratio of their areas is\[4:9\]. |
| Reason (R): The circumference of a circle of radius r is \[2\pi r\] and its area is \[\pi {{r}^{2}}\] . |
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] Both Assertion [a] and Reason (R) are true and reason (R) is the correct explanation of Assertion (A). |
| Given, \[\frac{2\pi {{r}_{1}}}{2\pi {{r}_{2}}}=\frac{2}{3}\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{2}{3}\] |
| Now, ratio of their areas be |
| \[\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}=\frac{r_{1}^{2}}{r_{2}^{2}}={{\left( \frac{2}{3} \right)}^{2}}=\frac{4}{9}\] |
| Also, circumference of circle \[=2\pi r.\] |
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