Question

The radius of two circles are 9cm and 12cm. Find the radius of a circle whose area is equal
to the sum of the areas of these two circles.​

Answer 1

Answer :

The radius of the circle whose area is equal to the sum of the areas of these two circles is 15 cm

Step-by-step explanation :

Given :

The radius of two circles are 9cm and 12cm

To find :

the radius of a circle whose area is equal  to the sum of the areas of these two circles.​

Solution :

Let

• r₁ = 9 cm
• r₂ = 12 cm

Area of circle of radius 9 cm :

 A₁ = πr₁²

 A₁ = π × (9)²

 A₁ = π × 81

 A₁ = 81π cm²

Area of circle of radius 12 cm :

 A₂ = πr₂²

 A₂ = π × (12)²

 A₂ = π × 144

 A₂ = 144π cm²

Let r₃ be the radius of a circle whose area is equal  to the sum of the areas of these two circles.​

Area of circle or radius r₃ cm :

  A₃ = πr₃²

   A₃ = A₁ + A₂

  πr₃² = 81π + 144π

    r₃² = 81 + 144

    r₃² = 225

    r₃² = 15²

    r₃ = 15 cm

Therefore, The radius of the circle whose area is equal to the sum of the areas of these two circles is 15 cm

Answer 2

Answer :♥️

The radius of the circle whose area is equal to the sum of the areas of these two circles is 15 cm

Step-by-step explanation :

Given :

The radius of two circles are 9cm and 12cm

To find :

the radius of a circle whose area is equal  to the sum of the areas of these two circles.

Solution :

Let

r₁ = 9 cm

r₂ = 12 cm

Area of circle of radius 9 cm :

 A₁ = πr₁²

 A₁ = π × (9)²

 A₁ = π × 81

 A₁ = 81π cm²

Area of circle of radius 12 cm :

 A₂ = πr₂²

 A₂ = π × (12)²

 A₂ = π × 144

 A₂ = 144π cm²

Let r₃ be the radius of a circle whose area is equal  to the sum of the areas of these two circles.

Area of circle or radius r₃ cm :

  A₃ = πr₃²

   A₃ = A₁ + A₂

  πr₃² = 81π + 144π

    r₃² = 81 + 144

    r₃² = 225

    r₃² = 15²

    r₃ = 15 cm

Therefore, The radius of the circle whose area is equal to the sum of the areas of these two circles is 15 cm

Hope it helps you♥️