Question

The ratio between the diameters of two circles is $5:7$. The ratio between their areas is _____.

• A. $5:7$
• B. $25:49$
• C. $7:5$
• D. $49:25$

Answer 1

The correct option is B

$25:49$

Let the diameters of the two circles be $5x$ and $7x$

$\therefore$ Their radius are $\frac{5x}{2}$ and $\frac{7x}{2}$

$\frac{Are{a}_1}{Are{a}_2}=\frac{\pi {\left(\frac{5x}{2}\right)}^2}{\pi {\left(\frac{7x}{2}\right)}^2}$

=$\frac{\frac{25x^2}{4}}{\frac{49x^2}{4}}$

= $\frac{25}{49}$

Therefore the ratio of their areas $=25:49$