It is proposed to build a single circular par | vedclass

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(D) Area of the first circular park with diameter $d_1 = 16 \, m$ is $A_1 = \pi r_1^2 = \pi (8)^2 = 64\pi \, m^2$,where $r_1 = 8 \, m$.Area of the sec

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$10$

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(D) Area of the first circular park with diameter $d_1 = 16 \, m$ is $A_1 = \pi r_1^2 = \pi (8)^2 = 64\pi \, m^2$,where $r_1 = 8 \, m$.Area of the second circular park with diameter $d_2 = 12 \, m$ is $A_2 = \pi r_2^2 = \pi (6)^2 = 36\pi \, m^2$,where $r_2 = 6 \, m$.Let the radius of the new circular park be $R$. According to the problem,the area of the new park is equal to the sum of the areas of the two parks:$\pi R^2 = A_1 + A_2$$\pi R^2 = 64\pi + 36\pi$$\pi R^2 = 100\pi$$R^2 = 100$$R = \sqrt{100} = 10 \, m$.Thus,the radius of the new park is $10 \, m$.

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 (in $m$)

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