Question

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Answer 1

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Radius of 1st circle = 8 cm (given)

∴ Area of 1st circle = π(8)2 = 64π

Radius of 2nd circle = 6 cm (given)

∴ Area of 2nd circle = π(6)2 = 36π

So,

The sum of 1st and 2nd circle will be = 64π+36π = 100π

Now, assume that the radius of 3rd circle = R

∴ Area of the circle 3rd circle = πR2

It is given that the area of the circle 3rd circle = Area of 1st circle + Area of 2nd circle

Or, πR2 = 100πcm2

R2 = 100cm2

So, R = 10cm

Answer 2

Answer:

• 10 cm

Step-by-step explanation:

Given :-

• Radii of two circles are 8 cm and 6 cm.

To find :-

• Radius of the circle which has area equal to the sum of the area of the two circles.

Solution :-

⇒ Radius of first circle = 8 cm

⇒ Radius of second circle = 6 cm

We are given with radii of two circles and are asked to find the radius of circle which has an area equal to the sum of the areas of the two circles.

⟹ Areas of two circles :

1. π(8)²

2. π(6)²

Now, their sum is equal to area of circle.

⇒ π(8)² + π(6)² = πr²

⇒ π(64) + π(36) = πr²

⇒ 64π + 36π = πr²

⇒ 100π = πr² (π get cancelled)

⇒ 100 = r²

⇒ r = √100

⇒ r = 10

∴ Radius of the circle which has an area equal to the sum of areas of two circles with radius 8 cm and 6 cm respectively is 10 cm.

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