| The diameters of two circles are the side of a square and the diagonal of the square. The ratio of the areas of the smaller circle and the larger circle is [SSC (CGL) 2013] |
A) \[1:4\]
B) \[\sqrt{2}:\sqrt{3}\]
C) \[1:\sqrt{2}\]
D) \[1:2\]
Correct Answer: D
Solution :
| Diagonal of a square\[=\sqrt{2}\times \text{Side}\] |
| \[\therefore \]Ratio of area of smaller circle to larger circle \[=\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}\] |
| \[=\frac{\pi \times {{\left( \frac{a}{2} \right)}^{2}}}{\pi \times {{\left( \frac{\sqrt{2}a}{2} \right)}^{2}}}=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}=1:2\] |
| [here, a = diameter of smaller circle] |
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