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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

A
10 m
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B
15 m
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C
20 m
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D
24 m
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Solution

## The correct option is B 10 mThe radius of one park r1=12×16 m=8 m & that of another one r2=12×12 m=6 m.∴ The sum of their areas =πr12+πr22=π(r12+ r22)=π(82+62)m2=100πm2. Again, let the radius of the proposed park be r. ∴ Its area =πr2. ∴ By the given condition πr2=100π m⇒r=10 m.

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