Question

Two circles have areas in the ratio 49 : 81. What is the ratio of their circumferences?

• A. 7:9
• B. 9:7
• C. 14:9
• D. 7:18

Answer 1

The correct option is A 7:9

Given, the ratio of areas of two circles is 49 : 81.

Let the radii of the two cicles be $r_1$ and $r_2$ respectively.

So, the area of first circle
$=\pi r_1^2$

The area of the second circle
$=\pi r_2^2$

Ratio of their areas = 49 : 81

$\therefore \pi r_1^2:\pi r_1^2=49:81$

$\Rightarrow r_1^2:r_2^2=49:81$

$\Rightarrow r_1:r_2=7:9$

Let the radii of the two circles be $7x$ and $9x$.

So the circumference of first circle
= 2 π $r_1$ = 2 π x 7$x$ = 14 π $x$

The circumference of the second circle = 2 π $r_2$ = 2 π x 9$x$ = 18 π $x$

The ratio of the circumferences of the two circles
= 14 π $x$ : 18 π $x$
= 14 : 18
= 7 : 9