Question

What will be the circumference of a circle having area 9 times the area of a circle with diameter 8 cm?

• A. 88 cm
• B. 70 cm
• C. 72.51 cm
• D. 75.36 cm

Answer 1

The correct option is D

75.36 cm

Let $r_1$ and $r_2$ be radii of two circles such that area of circle of radius $r_1$ is 9 times the area of circle of radius $r_2$.

$r_2=\frac{8}{2}$ cm = 4 cm

And we know that, area of a circle= $\pi r^2$
where r is its radius

Therefore, $\pi r_1^2$ = 9$\pi r_2^2$

$\Rightarrow$ $\pi r_1^2$ = 9$\pi \times 4^2$

$\Rightarrow$ $r_1^2$ = 144

$\Rightarrow$ $r_1$ = $\pm$ 12

Here, radius of the circle cannot be negative.

$\therefore$ $r_1=12cm$

Circumference of the circle of radius $r_1$
= 2$\pi r_1$ = 2 x 3.14 x 12 = 75.36 cm