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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. Find the radius of the new park.
Given: A single circular park equal in area to the sum of areas of two circular parks of diameters $16\ m$ and $12\ m$.
To do: To find the radius of the new park.
Solution:
Let the radius of new park be $r$.
Therefore, Area of new circular park$=$Sum of the two circular park
$\Rightarrow \pi r^2=\pi(8)^2+\pi(6)^2$
$\Rightarrow \pi r^2=64\pi+36\pi$
$\Rightarrow \pi r^2=100\pi$
$\Rightarrow r^2=100$
$\Rightarrow r=10\ m$
Thus, the radius of new park $10\ m$.
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