Question

If the circumference of a circular sheet is $154m$, find its radius. Also find the area of the sheet. (Take $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Step 1: Find the radius of the circle

Given that the circumference of a circular sheet is $154m$

Let $r$ be the radius of the circle .

We know that the

$$\begin{gathered} \mathrm{Circumference}\mathrm{of}\mathrm{circle}=2\mathrm{\pi r} \\ \Rightarrow 154=2·\frac{22}{7}·\mathrm{r} \\ \Rightarrow \mathrm{r}=\frac{49}{2} \\ \Rightarrow \mathrm{r}=24.5 \end{gathered}$$

Therefore, the radius of the circle is $24.5m$

Step 2: Find the area of the circle

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{circle}={\mathrm{\pi r}}^2 \\ \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{circle}=\frac{22}{7}·{\left(\frac{49}{2}\right)}^2 \\ \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{circle}=1886.5 \end{gathered}$$

The area of the circle is $1886.5m^2$

Hence, the radius of the circle is $24.5m$ and the area is $1886.5m^2$.