Question

Find the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radii $15cm$ and $8cm$

Answer 1

Step: Finding the radius of circle

Let, radius of circle $=r$

Circumference of circle $=2\pi r\dots \left(i\right)$

Given, radii of two circles are $15cm$ and $8cm$.

Then, circumference for $C_1=2\pi \left(15\right)\dots \left(ii\right)$

Circumference for $C_2=2\pi \left(8\right)\dots \left(iii\right)$

From equation $\left(1\right),\left(2\right)$ and $\left(3\right)$ :

$\because 2\pi r=2\pi \left(15\right)+2\pi \left(8\right)$ (Given condition)

$\Rightarrow r=15+8$

$\therefore r=23cm$

Hence, radius of circle is $23cm$.