| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion If the circumference of two circles are in the ratio 2 : 3, then ratio of their areas is 4 : 9. |
| Reason The circumference of a circle of radius r is \[2\pi r\] and its area is \[\pi {{r}^{2}}\]. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is false.
D) A is false; R is true.
Correct Answer: A
Solution :
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 area will be \[\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}={{\left( \frac{2}{3} \right)}^{2}}=\frac{4}{9}\] Also, circumference of circle \[=2\pi r\]
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