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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.

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detailed solution

Correct option is A

Let us given that, 

Radius of the first circle = 8 cm

Radius of the second circle = 6 cm

We know that, Area of a circle = πr2

Consider,

The radius of the third circle is r.

Area of 1st circle =  πr2π×× 8 = 64π

Area of 2nd circle = πr2=  π×× 6 = 36π

Area of 3rd circle = πr2

Circumference of 3rd circle = 2ππ

Now, it is given that

Area of 3rd circle = Area of 1st circle  + Area of 2nd circle

πr2 =  64π + 36π

πr2  = 100π

r2  = 100

r =  ±10

Hence, The radius of the circle having an area equal to the sum of the areas of the two circles is 10 cm.

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detailed solution

Correct answer is 1

Let us given that, 

Radius of the first circle = 8 cm

Radius of the second circle = 6 cm

We know that, Area of a circle = πr2

Consider,

The radius of the third circle is r.

Area of 1st circle =  πr2π×× 8 = 64π

Area of 2nd circle = πr2=  π×× 6 = 36π

Area of 3rd circle = πr2

Circumference of 3rd circle = 2ππ

Now, it is given that

Area of 3rd circle = Area of 1st circle  + Area of 2nd circle

πr2 =  64π + 36π

πr2  = 100π

r2  = 100

r =  ±10

Hence, The radius of the circle having an area equal to the sum of the areas of the two circles is 10 cm.

Talk to our academic expert!

+91

Are you a Sri Chaitanya student?

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