Question

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

Answer 1

Solution :-

Let the radius of the third circle be R.

Area of the circle with radius R = πR²

Area of the circle with radius 8 cm = π × 82 = 64π cm²

Area of the circle with radius 6 cm = π × 62 = 36π cm²

Sum of the area of two circles

= 64π cm² + 36π cm²

= 100π cm²

Area of the third circle = πR² = 100π cm²

⇒ πR² = 100π cm²

⇒ R² = 100 cm²

⇒ R = 10 cm

Thus, the radius of the new circle is 10 cm.

Thanks ..!!

Answer 2

Radius of 1st circle = 8 cm (given)

∴ Area of 1st circle = π(8)2 = 64π

Radius of 2nd circle = 6 cm (given)

∴ Area of 2nd circle = π(6)2 = 36π

So,

The sum of 1st and 2nd circle will be = 64π+36π = 100π

Now, assume that the radius of 3rd circle = R

∴ Area of the circle 3rd circle = πR2

It is given that the area of the circle 3rd circle = Area of 1st circle + Area of 2nd circle

Or, πR2 = 100πcm2

R2 = 100cm2

So, R = 10cm