uptetd16p2 q124

124It 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. The radius of the new park would be

Option : A
Explanation : Let 'R' be the radius of the new circle. Area of new circular park = Area of circle 1 of diameter 16 m + Area of circle 2 of diameter 12 m
⇒ πR² = π(8)² + π(6)² [∵ R₁ = 16/2 = 8 R₂ = 12/2 = 6]
⇒ πR² = 64π + 36π
⇒ πR² = 100π
⇒ R² = 100 ⇒ R = 10 m

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