Question

the radii of two circles are 19cm and 9cm,respectively.find the circumference and radius of a circle which has its circumference equal to the sum of circumferences of the two circles.

Answer 1

C=c1+c2
2pie.R=2 pie. (19+9)
R=19+9
R=28cm

Answer 2

Given :-

The radius of the 1st circle = 19 cm

The radius of the 2nd circle = 9 cm

To Find :-

The radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

Solution :-

We know that,

r = Radius

c = Circumference

Given that, radius of the 1st circle = 19 cm

Then,

Circumference of the 1st circle =

$\sf 2 \pi \times 19 = 38$

Given that, radius of the 2nd circle = 9 cm

Then,

Circumference of the 2nd circle =

$\sf 2 \pi \times 9=18$

According to the question,

The sum of the circumference of two circles

$= \sf 38 \pi +18 \pi=56$

Let the radius of the 3rd circle be 'r'

So,

∴ The circumference of the 3rd circle =

$\sf 2 \pi$

Given that, sum of the circumference of two circles = circumference of the 3rd circle

Hence,

$</p><p>6 \pi=2 \pi r \\ </p><p></p><p>\sf r = 28 \ cm$

• Therefore, the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles is 28 cm9