Question

Find the circumference of circle whose area is 16 times the area of the circle with diameter 1.4 m.

Answer 1

Given that, area of a circle is $16$ times the area of another circle with diameter $1.4m$.

To find out: Circumference of the first circle.

Now, radius of the second circle $=\frac{1.4}{2}=0.7m$

We know that, area of a circle $=\pi r^2$

$\therefore$ Area of the second circle $=\frac{22}{7}\times 0.7\times 0.7$

$\Rightarrow 1.54m^2$

Then,

Area of first circle$=16\times 1.54=24.64m^2$

$\therefore \pi r^2=24.64$

$r^2=\frac{24.64}{\pi }$

$r^2=\frac{24.64}{\frac{22}{7}}$

$r^2=\frac{24.64\times 7}{22}$

$r^2=7.84$

$r=\sqrt{7.84}$

$r=2.8m$

Now, Circumference of circle $=2\pi r$

$=2\times \frac{22}{7}\times 2.8$

$=\frac{123}{7}$

$=17.6m$

Hence, the circumference of the circle is $17.6m$.