Question

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

Hint: We know the circumference of a circle is $2\pi r$. Find the radius of the circle from the circumference. After finding radius, find the area of a circle using the formula of area.

We know that circumference of a circle is equal to $2\pi r$, where r is the radius of the circle.
$\therefore$Circumference of circle = $2\pi r$.
We are given the value of circumference of the circle = 31.4cm.
We need to find the radius ‘r’ of the circle.
\begin{align} & \Rightarrow 2\pi r=31.4 \\ & r=\dfrac{31.4}{2\pi }=\dfrac{31.4}{2\times 3.14}=\dfrac{3.14\times 10}{2\times 3.14} \\ & =\dfrac{10}{2}=5cm \\ \end{align}
Hence, we got the radius of the circle as 5cm.
Now let us find the area of the circle.
We know the area of a circle is given by $\pi {{r}^{2}}$.
Area$=\pi {{r}^{2}}=\pi \times {{5}^{2}}=\pi \times 5\times 5$
$=3.14\times 25=78.5c{{m}^{2}}$
Hence, we got the radius of the circle as 5cm and the area of the circle as $78.5c{{m}^{2}}$respectively.

Note: To find the diameter of the circle you can take twice the radius of the circle i.e. diameter $=2\times$radius. We can find the area of the circle by directly substituting the value of diameter instead of radius.
radius$=\dfrac{diameter}{2}\Rightarrow r=\dfrac{d}{2}$, area$=\pi {{r}^{2}}=\pi \times {{\left( \dfrac{d}{2} \right)}^{2}}$
area$=\dfrac{\pi {{d}^{2}}}{4}$
$\therefore$ area of circle can be also said as $\dfrac{\pi {{d}^{2}}}{4}$.