Question

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15\mathrm{cm}$ and $18\mathrm{cm}$.

Answer 1

Step 1: Define the problem

Radius of first circle, $r_1=15\mathrm{cm}$

Radius of second circle, $r_2=18\mathrm{cm}$

Let $R$ be the radius of the bigger circle.

Step 2: Compute the radius of the bigger circle

The formula for finding the circumference of a circle is given as,

$\mathrm{C}=2\mathrm{\pi r}$

Where, $\mathrm{C}$ is the circumference and $\mathrm{r}$ is the radius of the circle.

Thus,

$$\begin{gathered} 2\mathrm{\pi }R=2\mathrm{\pi }{r}_{\mathit{1}}+2\mathrm{\pi }{r}_2 \\ 2\mathrm{\pi }R=2\mathrm{\pi }·15+2\mathrm{\pi }·18 \\ \Rightarrow 2\mathrm{\pi }R=2\mathrm{\pi }(15+18) \\ \Rightarrow R\mathit{=}15+18 \\ \Rightarrow R\mathit{=}33\mathrm{cm} \end{gathered}$$

Therefore, the radius of the bigger circle is $33\mathrm{cm}$.