The radii of two circles are 12 cm and 6cm respectively, find the radius of the circle having the area equal to the sum of the areas of the two circle.
Answers
Step-by-step explanation:
pi (12^2+6^2)= pi (×^2)
x^2 =180
x=6 root5
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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.