Question

The circumference of circle K is $\pi$. The circumference of Circle L is $4\pi$. What is the value of the ratio of their circumferences? Of their radii? Of their areas?

Answer 1

Step 1: Find the ratio of radius of both circle.

Given,

The circumference of circle K is $\pi$.

The circumference of circle L is $4\pi$.

As we know that the circumference of circle is $2\pi \mathrm{r}$.

So, the radius, $r_1$ of circle K is

$$\begin{gathered} \Rightarrow 2\pi r_1=\pi \\ \Rightarrow r_1=\frac{1}{2} \end{gathered}$$

And, the radius,$r_2$ of circle L is

$$\begin{gathered} \Rightarrow 2\pi r_2=4\pi \\ \Rightarrow r_2=2 \end{gathered}$$

Therefore, the ratio of radius of both circle is

$\Rightarrow \frac{r_1}{r_2}=\frac{1}{4}$

Step 2: Find the ratio of area of both circle.

As we know, the area of circle is $\pi r^2$

So, the ratio of area of circle K to the circle L will be

$\Rightarrow \frac{{\pi r_1}^2}{\pi {r_2}^2}=\frac{{\displaystyle \frac{1}{4}}}{4}=\frac{1}{16}$

Step 3: Final answer.

Hence, the ratio of radii and area of both circle are $\frac{1}{4}$ and $\frac{1}{16}$ respectively.