Question

Two small circular grounds of diameters 42 m and 26 m are to be replaced by a bigger circular ground. What would be the radius of the new ground if the new ground has the same area as two small grounds?

• A. 23 m
• B. 25.01 m
• C. 24.63 m
• D. 25 m

Answer 1

Answer:

C. 24.63 m

Solution:

Given:

The diameter of the two small circular grounds = 42 m and 26 m respectively

Formula Used:

Area of the circle = πR²

Calculation:

The radius of the 1st circle R₁ = 42/2  = 21 m

The radius of the 2nd circle R₂ = 26/2 = 13 m  

Total Area of the two small ground = π(R²₁ + R²₂) = π ( 21² + 13²) = π  × (441 + 169)

Total area = 610π m²

New ground area = 610π 

610π  = πR² 

⇒ R2 = 610

⇒ R = √610

⇒ R ≈ 24.63 m

∴ The radius of the new ground if the new ground has the same area as two small grounds is 24.63 m.