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#### 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                     (B) 15 m                     (C) 20 m                     (D) 24 m

Answer (A) 10 m

Solution

Diameter of first circle (D) = 16 m

Radius(R) =$\frac{16}{2}=8m$

Area =$\pi r^{2}=\pi \times 8 \times 8=64\pi$

Diameter of second circle (d) = 12 m

Radius(r) =$\frac{12}{2}=6m$

Area =$\pi r^{2}=\pi \times 6 \times 6=36\pi$

Let radius of new park = R1

Area =$\pi R_{1}^{2}$

According to question

$64\pi+36\pi=\pi R_{1}^{2}\\ 100\pi=\pi R_{1}^{2}\\ 100= R_{1}^{2}\\ \pi R_{1}=\pm 10$

R = – 10 is not possible because Radius must be positive.

Hence Radius is 10m