Question

The circumference of a circle exceeds its diameter by 45 cm. Find the circumference of the circle.

Answer 1

Let the radius of the circle be r.
Now,
Circumference = Diameter + 45
$$\begin{gathered} \Rightarrow 2\mathrm{\pi }r=2r+45 \\ \Rightarrow 2\mathrm{\pi }r-2r=45 \\ \Rightarrow 2r\left(\frac{22}{7}-1\right)=45 \\ \Rightarrow 2r\times \frac{15}{7}=45 \\ \Rightarrow r=10.5\mathrm{cm} \end{gathered}$$
∴ Circumference = Diameter + 45 = 2(10.5) + 45 = 66 cm
Hence, the circumference of the circle is 66 cm.