the radii of two circles are 8cm and 6cm respectively find the radius of the circle having area equal to the sum of the area of the two circles
Answers
Step-by-step explanation:
given radius of one circle=8cm
radius of another circle=6cm
let us assume the radius of the circle whose area is equal to the sum of area of the other two circles as R1.
Therefore, according to question,
πR1×R1=π8×8+π6×6.
R1×R1=100(cancelling π out)
R1=10cm.
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.