Question

Two circles have circumference in the ratio $6:7$. Find the ratio of their areas.

• A. $36:49$
• B. $49:36$
• C. $30:49$
• D. $40:39$

Answer 1

The correct option is A $36:49$

Given: Ratio of circumference $=6:7$

Let the radius of the first circle be $r$ and the radius of the second circle be $R$.

Circumference of a circle $=2\pi r$

$\frac{2\pi r}{2\pi R}=\frac{6}{7}$

$\frac{r}{R}=\frac{6}{7}$ $...\left(1\right)$

Area of first circle $=\pi r^2$

Area of second circle $=\pi R^2$

Ratio will be,
$=\frac{\pi r^2}{\pi R^2}$

$=\frac{r^2}{R^2}$

$={\left(\frac{r}{R}\right)}^2$

From $...\left(1\right)$

$={\left(\frac{6}{7}\right)}^2=\frac{36}{49}=36:49$