Question

Unless stated otherwise use $\pi =\frac{22}{7}$.

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 circumference of the two circles.

Answer 1

For a given:-

$1-$ circle (Radius $r_1=19$$cm$)

$2-$ circle (Radius $r_2=9cm$)

According to the problem$:-$

Circumference of the required circle is equal to the sum of circumference of two circles.

Circumference (Small circle)

$=2\pi r_1$

$=2\pi \times 19$

$=38\pi$

Similarly,

Circumference (Large circle)

$=2\pi r_1$

$=2\pi \times 9$

$=18\pi$

Now, according to condition-

$2\pi r=18\pi +38\pi$

$2\pi r=56\pi$

$r=\frac{56\pi }{2\pi }=28\left(Radiusofnewcircle\right)$