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Question
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 ______.
Options
10 m
15 m
20 m
24 m
Solution
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 10 m.
Explanation:
Let D1 be the diameter of the first circular park = 16 m
∴ Radius R1 of first circular park = 8 m
Area of first circular park = πr2 = π(8)2 = 64 π m2
Let D2 be the diameter of the second circular park = 12 m
∴ Radius R2 of second circular park = 6 m
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 = 64π + 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 10 m.
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