Question

5. The radii of two circles are 16 cm and 12 cm respectively. Find the radius of the
circle having area equal to the sum of the areas of the two circles.​

Answer 1

Let the radius of required circle is r cm.

So, πr

2

=πr

1

2

+πr

2

2

r

2

=r

1

2

+r

2

2

r

2

=(8)

2

+(6)

2

r

2

=100

r=10cm

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Answer 2

Answer :-

The radius of the circle having area equal to the sum of the areas of the two circles = 20 cm

Step by step explanation :-

Given:-

• Radius of first circle(r₁) = 16 cm.
• Radius of second circle(r₂) = 12 cm.

Have to Find :-

Find the radius of the circle having area equal to the sum of the areas of the two circles.

Solution :-

So , we consider the radius of circle be " R " $cm$

As we know in the question , It is said that 'radius of the circle having area equal to sum of areas of other two circles .

Hence , from this we get :-

↬ πR² = πr₁ + πr₂

Taking π as common :-

↬ πR² = π(r₁ + r₂)

Now , substituting the values in the above formula :-

↬ πR² = π (16² + 12²)

↬ πR² = π (256 + 144 )

↬ πR² = π (400)

π cancels π ., then

↬ R² = 400 cm

↬ R = √400

↬ R = 20 cm.

Thus, Radius of the circle = 20cm.

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