**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 would be

(a) 10 m

(b)15m

(c) 20 m

(d) 24 m

**Solution:**

(a) Area of first circular park, whose diameter is $16 \mathrm{~m}$

$=\pi r^{2}=\pi\left(\frac{16}{2}\right)^{2}=64 \pi \mathrm{m}^{2}$ $\left[\because r=\frac{d}{2}=\frac{16}{2}=8 \mathrm{~m}\right]$

Area of second circular park, whose diameter is $12 \mathrm{~m}$

$=\pi\left(\frac{12}{2}\right)^{2}=\pi(6)^{2}=36 \pi m^{2}$ $\left[\because r=\frac{d}{2}=\frac{12}{2}=6 m\right]$

According to the given condition,

Area of single circular park = Area of first circular park + Area of second circular park

$\pi R^{2}=64 \pi+36 \pi \quad[\because R$ be the radius of single circular park $]$

$\Rightarrow \quad \pi R^{2}=100 \pi \Rightarrow R^{2}=100$

$\therefore \quad R=10 \mathrm{~m}$