Question

The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is
(a) 3 : 2
(b) 4 : 9
(c) 2 : 3
(d) 81 : 16

Answer 1

Let the the radii of the two circles be r and R, the circumferences of the circles be c and C and the areas of the two circles be a and A.
Now,
$$\begin{gathered} \frac{a}{A}=\frac{9}{4} \\ \Rightarrow \frac{\mathrm{\pi }{r}^2}{\mathrm{\pi }{R}^2}={\left(\frac{3}{2}\right)}^2 \\ \Rightarrow \frac{r}{R}=\frac{3}{2} \end{gathered}$$
Now, the ratio between their circumferences is given by
$$\begin{gathered} \frac{c}{C}=\frac{2\mathrm{\pi }r}{2\mathrm{\pi }R} \\ =\frac{r}{R} \\ =\frac{3}{2} \end{gathered}$$
Hence, the correct answer is option (a)