Question

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is ______.

विकल्प

• 31 cm

• 25 cm

• 62 cm

• 50 cm

Answer 1

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.

Explanation:

Let r₁ = 24 cm and r₂ = 7 cm

∴ Area of first circle = `π"r"_1^2`

= π(24)²

= 576π cm²

And area of second circle = `π"r"_2^2`

= π(7)²

= 49π cm²

According to the given condition,

Area of circle = Area of first circle + Area of second circle

∴ πR² = 576π + 49π   ...[Where, R be radius of circle]

⇒ R² = 625

⇒ R = 25 cm

∴ Diameter of a circle = 2R

= 2 × 25

= 50 cm