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 ?
Answer & explanation
Correct answer: option 1
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