Question

The radii of the circles are 20 cm and 10 cm. Find the radius of the circle whose circumference is equal to the sum of the circumferences of the two circles​

Answer 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

we know that

the circumference of circle = 2πr

where r is the radius

now.

the circumference of circle of radius 15 cm = 2π×15= 30π cm

&

the circumference of circle of radius 18cm = 2π×18 = 36π

According to question

the circumference of circle whose radius is r = 30π+36π = 66π

=> 2πr =66π

=> r = 33 answer

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Answer 2

Given :-

The radii of the circle are 20 cm & 10 cm

Required to find :-

• Radius of the circle whose circumference is equal to the sum of the circumferences of the two circles ?

Formula used :-

$\boxed{\tt{\bf{ Perimeter \ of \ the \ circle = 2 \pi r }}}$

Solution :-

Given Information :-

The radii of the circle are 20 cm & 10 cm

we need to find the radius of the circle whose circumference is equal to the sum of the circumferences of the two circles .

So,

Let the 2 circles be ;

Circle - 1

Radius = 20 cm

Circle - 2

Radius =10 cm

Here,

we need to find the circumference of each circle respectively .

So,

Using the formula ;

$\boxed{\tt{\bf{ Perimeter \ of \ the \ circle = 2 \pi r }}}$

This implies ;

Perimeter of the 1st circle ;

Perimeter = 2 x 3.14 x 20

Perimeter = 40 x 3.14

Perimeter = 125.6 meters

Hence,

• Perimeter of the 1st circle = 125.6 meters

Similarly,

Perimeter of the 2nd circle ;

Perimeter = 2 x 3.14 x 10

Perimeter = 2 x 31.4

Perimeter = 62.8 meters

Hence,

• Perimeter of the 2nd circle = 62.8 meter

But,

Actually we need to find the radius of the circle whose circumference is the sum of the circumferences of 2 circles .

So,

This implies ;

Circumference of the required circle =

perimeter of 1st circle + perimeter of 2nd circle

=> 125.6 + 62.8

=> 188.4 meters

Hence,

• Circumference of the required circle = 188.4 meters

Now,

Let's find the radius of the circle ;

Using the same formula ;

Here , let's take the value of r as r only !

This implies ;

Perimeter = 2 π r

188.4 = 2 x 3.14 x r

188.4 = 6.28 x r

6.28 x r = 188.4

r = 188.4/6.28

r = 18840/628

r = 30 meters

Hence,

• Radius = 30 meters

Therefore ;

Radius of the circle ( r ) = 30 meters