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.

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