Question

The circumference of a circle exceeds its diameter by 16.8 cm. Find the circumference of the circle.

Answer 1

Circumference of a circle = $2\mathrm{\pi r}$
Diameter, d = 2r
Thus, we have:
$d+16.8=2\mathrm{\pi r}$
$$\begin{gathered} \Rightarrow 2r+\hspace{0.17em}16.8=2\mathrm{\pi r} \\ \Rightarrow 2\mathrm{\pi r}-2\mathrm{r}=16.8 \\ \Rightarrow 2\mathrm{r}\left(\mathrm{\pi }-1\right)=16.8 \\ \Rightarrow \mathrm{r}=\frac{16.8}{2\left(\mathrm{\pi }-1\right)} \\ \Rightarrow \mathrm{r}=\frac{16.8}{2\left({\displaystyle \frac{22}{7}}-1\right)} \\ \Rightarrow \mathrm{r}=\frac{16.8}{2\left({\displaystyle \frac{22-7}{7}}\right)} \\ \Rightarrow \mathrm{r}=\frac{16.8\times 7}{44-14} \\ \Rightarrow \mathrm{r}=\frac{117.6}{30} \\ \Rightarrow \mathrm{r}=3.92\mathrm{cm} \end{gathered}$$

Now,
Circumference of the circle = $2\times \frac{22}{7}\times 3.92$

= 24.64 cm