Question

If the diameter of a circle is equal to the diagonal of a square, then the ratio of their areas is
(a) $7:1$ (b) $1:1$ (c) $11:7$ (d) $22:7$

Answer 1

The correct option is (c): $11:7$

Let ${}^{\prime }{r}^{\prime }$ and ${}^{\prime }{a}^{\prime }$ be the diameter of the circle and side of the square respectively. Then
Diameter of circle $=2r$
Diagonal of square $=\sqrt{a}$
Now, as per the question
Diameter of circle = Diagonal of square
$2r=\sqrt{a}$

$\Rightarrow a=4r^2$ [On squaring both sides]
Therefore
$\frac{\text{Area of circle}}{\text{Area of square}}$ $=\frac{\pi r^2}{a^2}$

$=\frac{\frac{22}{7}\times r^2}{2r^2}=\frac{11}{7}$