Question

The circumference of a circle is $31.4\mathrm{cm}$. Find the radius and the area of the circle? (Take $\mathrm{\pi }=3.14$)

Answer 1

Step 1: Find the radius of the circle.

Given : Circumference of a circle $=31.4cm$

Circumference of a circle $=2\mathrm{\pi r}$

$\Rightarrow$ $31.4=2\times 3.14\times \mathrm{r}$

$\Rightarrow$ $31.4=6.28\times \mathrm{r}$

$\Rightarrow$ $\mathrm{r}=\frac{31.4}{6.28}$

$\Rightarrow$ $\mathrm{r}=5\mathrm{cm}$

Step 2: Find the area of the circle.

Area of the circle $={\mathrm{\pi r}}^2$

$\Rightarrow$ $=3.14\times 5^2$

$\Rightarrow$ $=3.14\times 25$

$\Rightarrow$ $=78.5{\mathrm{cm}}^2$

Therefore, area of a circle is $78.5{\mathrm{cm}}^2$and radius of circle is $5\mathrm{cm}$.