Question

The radii of two circle are 8 cm and 6 cm respectively Find the radius of circle having area equal to the sum of area of two circle

Answer 1

Solution :

Let the two Radius of the Circle r1 and r2 respectively

r1 = 8 cm

r2 = 6 cm

According to the Question

Radius of the Circle having area = Sum of area of the two Circle

area ( c1 + c2 ) = area ( c3)

$(\pi r^2)_1 + (\pi r^2)_2 = (\pi r^2)_3 \\\\\pi ( 8^2 + 6^2) =( \pi r^2)_3$

$r_3 = \sqrt{(8)^2 + (6)^2 }$

= $\sqrt{64 + 36 }$

= $\sqrt{100}$

= 10 cm

Radius of r_3 = 10 cm

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.

hope it is helpful for u