Question : If the length of a side of the square is equal to that of the diameter of a circle, then the ratio of the area of the square and that of the circle is:
Option 1: 14 : 11
Option 2: 7 : 11
Option 3: 11 : 14
Option 4: 11 : 7
Correct Answer: 14 : 11
Solution :
Let the side of the square be $s$.
$\therefore$ Area of this square = $s^2$
Diameter of the circle = $s$
So, the radius of the circle = $\frac{s}{2}$
Area of the circle = $\pi (\frac{s}{2})^2$
$\therefore$ Required ratio = $\frac{s^2}{\pi (\frac{s}{2})^2}=\frac{4\times 7}{22}=\frac{14}{11}$
Hence, the correct answer is 14 : 11.
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