It is proposed to build a single circular par | vedclass

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Question

Area of first circular park, whose diameter is $16\, m$

$=\pi r^{2}=\pi\left(\frac{16}{2}\right)^{2}=64 \pi\, m ^{2} \quad\left[\because r=\frac{d}

Vedclass · Accepted Answer

$10$

Vedclass · Answer

Area of first circular park, whose diameter is $16\, m$

$=\pi r^{2}=\pi\left(\frac{16}{2}ight)^{2}=64 \pi\, m ^{2} \quad\left[\because r=\frac{d}{2}=\frac{16}{2}=8 \, m ight]$

Area of second circular park, whose diameter is $12 \,m$

$=\pi\left(\frac{12}{2}ight)^{2}=\pi(6)^{2}=36 \pi \, m^{2} \quad\left[\because r=\frac{d}{2}=\frac{12}{2}=6 \, m ight]$

According to the given condition,

Area of single circular park $=$ Area of first circular park $+$ Area of second circular park

$\pi R^{2}=64 \pi+36 \pi$ $[\because R$ be the radius of single circular park]

$\Rightarrow \pi R^{2}=100 \pi \Rightarrow R^{2}=100$

$	herefore \quad R=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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