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 the two small grounds ?

24.63 m

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

We know that,

Area of the circle = πR²

The radius of the 1st circle R₁ = \(\frac{42}{2}\)= 21 m

The radius of the 2nd circle R₂ = \(\frac{26}{2}\)= 13 m  

So, the total Area of the two small grounds = π(R²₁ + R²₂) = π ( 21² + 13²) = π  × (441 + 169)

Total area = 610π m²

New ground area = 610π 

610π  = πR² 

= R² = 610

= R = \(\sqrt {610}\)

= R = 24.63 m