Question

find the radius of a circle whose area is equal to the sum of the areas of four other circle of radius 5m,6m,8m and 10m​

Answer 1

Given :

• Radius of four circles :-

• Radius of first circle = 5 m
• Radius of second circle = 6 m
• Radius of third circle = 8 m
• Radius of fourth circle = 10 m

To find :

• Radius of circle whose area is equal to the sum of the areas of four circles.

Concept :

Formula to calculate area of circle :-

• Area of circle = πr²

where,

• Take π = 22/7

• r denotes the radius of the circle

Solution :

According to the question :-

→ Area of 1st circle + Area of 2nd circle + Area of 3rd circle + Area of 4th circle = Area of larger circle

→ πr₁² + πr₂² + πr₃² + πr₄² = πR²

Here, r₁, r₂, r₃ and r₄ denote the radius of the four circles and R denotes the radius of the larger circle.

→ Taking π common from both the sides :-

→ π(r₁² + r₂² + r₃² + r₄²) = π(R²)

→ π will get cancelled :-

→ r₁² + r₂² + r₃² + r₄² = R²

→ Substituting the value of r :-

→ 5² + 6² + 8² + 10² = R²

→ 25 + 36 + 64 + 100 = R²

→ 225 = R²

→ Taking square root on both the sides :-

→ √225 = R

→ √(15 × 15) = R

→ ± 15 = R

As we know, the radius of circle cannot be nagative. So, the negative sign will get rejected.

→ ± 15 Reject - ve = R

→ 15 = R

→ The value of R = 15 m

Therefore, radius of a circle whose area is equal to the sum of the areas of four other circle of radius 5m, 6m, 8m and 10m is 15 m