Question

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

Answer 1

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The radii of two circles are 19 cm and 9 cm 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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The radius of the 1st circle = 19 cm (given)

∴ Circumference of the 1st circle = 2π×19 = 38π cm

The radius of the 2nd circle = 9 cm (given)

∴ Circumference of the 2nd circle = 2π×9 = 18π cm

So,

The sum of the circumference of two circles = 38π+18π = 56π cm

Now, let the radius of the 3rd circle = R

∴ The circumference of the 3rd circle = 2πR

It is given that sum of the circumference of two circles = circumference of the 3rd circle

Hence, 56π = 2πR

Or, R = 28 cm.

Answer 2

☆ Solution ☆

Given :-

• The radii of two circles are 19 cm and 9 cm respectively.

To Find :-

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

Step-by-Step-Explaination :-

Here,

The radii of two circles are r1= 19 cm and r2 =9 cm.

Then,

The sum of circumferences of these two circles

= 2πr1 + 2πr2

= 2π (r1 + r2)

=2π (19 + 9) cm

= 2π (28) cm

Let the radius of the third circle be R cm.

Then,

Circumference of the third circle = 2πR cm.

According to data,

2πR = 2r (28)

Therefore,

R = 28 cm

Thus,

The radius of the required circle is 28 cm.