It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
Let D1 be the diameter of the first circular park = 16m
∴ Radius R1 of first circular park = 8m
Let D2 be the diameter of the second circular park = 12m
∴ Radius R2 of second circular park = 6m
Area of first circular park = πr2 = π(8)2 = 64 π m2
Area of second circular park = πr2 = π(6)2 = 36 π m2
Now, we are given that,
Area of single circular park = Area of first circular park + Area of second circular park
∴ πR2 = 64 π + 36π = 100π
(where R is the radius of the single circular park)
πR2 = 100π ⇒ R2 = 100 ⇒ R = 10
∴ Radius of the single circular park will be 10m.