Question

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





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Answer 1

Let the radius of required circle =r cm

Radius of 1st circle r

1

=9 cm

Radius of 2nd circle r

2

=19 cm

As per the question

Circumference of the required circle = Sum of circumference of two circles

Circumference of small circle =2πr

1

=2π×9

=18π

Circumference of small circle =2πr

2

=2π×19

=38π

Now,

Circumference of the required circle = Sum of circumference of two circles

2πr=18π+38π

2πr=58π

r=

2π

56π

r=28 cm

Hence, radius of new circle is 28 cm.

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

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

Then,

Circumference of the 2nd circle = $\sf 2 \pi \times 9=18 \pi \ cm$

According to the question,

The sum of the circumference of two circles = $\sf 38 \pi +18 \pi=56 \pi \ cm$

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

So,

∴ The circumference of the 3rd circle = $\sf 2 \pi r$

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

Hence,

$\sf 56 \pi=2 \pi r$

$\sf r = 28 \ cm$

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