Question

the radii of 2 circles are 8cm and 6cm respectively
Find the radius of the circle having area equal to the sum of the areas of the 2 circles.

Answer 1

Area of circle 1= π*r squared
                       =22*8*8/7
                       =201.06 cm squared
Area of circle 2=π*r sqaured
                       =22*6*6/7
                       =113.10 cm squared
total area= (201.06+113.10) cm squared
              = 314.16 cm squared
Now, we know the area of our circle, we will find the radius using the following expression:-
 
π*r squared=314.16 cm squared
r= 10 cm

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Answer 2

Radius of 1st Circle = 8cm

Area of 1st Circle = πr²1

Radius of 2nd Circle= 6cm

Area of 2nd Circle = πr²2

Area of both circle= πr²1 + πr²2

= π(r²1+r²2)

= 22/7 (8²+6²)

=22/7 (64+36)

=22/7×100 = 2200/7 cm²

Area of bigger Circle =2200/7cm²

πr² = 2200/7

22/7 ×r² = 2200/7

r² = 2200/7

_________

22/7

r² = 2200/7 × 7/22

r²= 100

r = √100

r = 10cm.

Hence, the radius of bigger circle = 10cm.

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