It is proposed to build a single circular park equal in area to the sum of areas of two circular par

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 is\

Professor PC Thomas Classes · Answer

(a): Let $r$ be the radius of new park. Diameter of first circular park $=16 \mathrm{~m}$\ ∴ Radius $\left(r_{1}ight)=8 \mathrm{~m}$\ Diameter of second circular park = 12 m\ $	herefore \quad$ Radius $\left(r_{2}ight)=6 \mathrm{~m}$\ Now, area of new park = Sum of area of two circular parks\ $\Rightarrow \pi r^{2}=\pi\left(r_{1}^{2}+r_{2}^{2}ight) \Rightarrow r^{2}=8^{2}+6^{2}=100$\ $\Rightarrow r=\sqrt{100}=10 \mathrm{~m} \quad$ (since radius cannot be negative)\