Question

The radius of one circular field is 7 m and that of another is 25 m. Find the radius of the
circular field whose area is equal to the difference of the areas of the first and second field.​

Answer 1

Answer:

Let small circle is C

1

and big circle is C

2

.

Given radius of C

1

=5m and radius of C

2

=13m.

Now area of circle is =πr

2

, where r is radius of circle.

Then, area of C

1

=π(5)

2

=25πm

2

−−−−−−(1)

Similarly, area of C

2

=π(13)

2

=169πm

2

−−−−−−(2)

Now, difference of both areas is =169π−25π=144πm

2

−−−−−−−(3)

Let circle C

3

has area equal to difference of area of C

2

and C

1

.

Let radius of C

3

=r

′

.

Then, area of C

3

=144πm

2

{from equation(3)}

So, πr

′

2

=144π

r

′

2

=144

r

′

=12

So, radius of cricle C

3

=12m

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