Question

The radii of two circles are $19cm$ and $9cm$ respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

Answer 1

Circumference of circle:

It is given that$,$

The radii of the two circles are $19cm$ and $9cm$ respectively

We have to find out the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

Radius $\left(r_1\right)=19cm$

Radius $\left(r_2\right)=9cm$

The formula of the circumference of circle $C=2\pi r.$

The circumference of a circle with a radius of $19cm$ is $$\begin{gathered} =2\pi \times 19 \\ =38\pi cm. \end{gathered}$$

The circumference of a circle with a radius of $9cm$ is $$\begin{gathered} =2\pi \times 9 \\ =18\pi cm. \end{gathered}$$

Total Circumference is $$\begin{gathered} =38\pi +18\pi \\ =56\pi cm \end{gathered}$$

Now using $C=2\pi r_3$ we will find $r_3$

$56\pi =2\pi \times r_3$

$56=2r_3$

$r_3=28cm$

Hence, the radius of the circle which has a circumference equal to the sum of the circumference of the given two circles is $28cm$