Question

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



Don't spam ​

Answer 1

Answer:

10 cm

Given:

• Radius of first circle = 8cm
• Radius of second circle = 6cm

To Find:

• Radius of the third circle having equal area as the sum of areas of first two circles.

Solution:

$\underline{\boxed{\rm Area\:of\: circle=\pi {r}^{2} }}$

Area of first circle

= πr²

= π (8 cm )²

= 64cm² π

Area of second circle

= πr²

= π ( 6 cm )²

= 36cm² π

Area of third circle

( let radius = r )

= πr²

According to the question:

Area of 3rd circle = Area of 1st + Area of 2nd circle

= πr² = 64cm² π + 36cm² π

= πr² = π ( 64cm² + 36cm² )

= r² = 64cm² + 36cm²

= r² = 100cm²

= r² = ( 10 cm )²

= r = √(10cm)²

= r = 10 cm

Radius of the circle is 10 cm

Answer 2

Here is ur 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