the radii of two circles are 12cm and 5cm respectively. find the radius of the circle having area equal to the areas of the two circles
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π r^2 + π r2^2 = π R^2
π(5 ×5 +12×12)square cm = π R^2
R^2 = (25+144) square cm
R^2 = 169 square cm
R = 13 cm
π(5 ×5 +12×12)square cm = π R^2
R^2 = (25+144) square cm
R^2 = 169 square cm
R = 13 cm
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1
Answer ✅✅✅
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.
hope it is helpful for u
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