Question

The radius of a circle whose area is equal to the sum of the areas of 2 circles with radii 6 cm and 8 cm is ______.

पर्याय

• 5 cm

• 10 cm

• 9 cm

• 15 cm

Answer 1

The radius of a circle whose area is equal to the sum of the areas of 2 circles with radii 6 cm and 8 cm is 10 cm.

Explanation:

Given:

• Radius of first circle r₁ = 6 cm
• Radius of second circle r₂ = 8 cm

Sum of areas of the two circles:

`πr_1^2 + πr_2^2`

= π(6² + 8²)

= π(36 + 64)

= π × 100

Let the radius of the new circle be (R).

Then, πR² = π × 100

⇒ R² = 100

⇒ R = 10 cm

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