Question

It is proposed to build a single 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 ___________.

Answer 1

Let the radius of the new circular park be r m.

Suppose the radii of two circular parks be r₁ m and r₂ m.

Diameter of the first circular park = 16 m

⇒ 2r₁ = 16

⇒ r₁ = 8 m

Diameter of the second circular park = 12 m

⇒ 2r₂ = 12

⇒ r₂ = 6 m

Now,

Area of the new circular park = Area of first circular park + Area of second circular park

$$\begin{gathered} \mathrm{\pi }{r}^2=\mathrm{\pi }{r}_1^2+\mathrm{\pi }{r}_2^2 \\ \Rightarrow r^2=r_1^2+r_2^2 \\ \Rightarrow r^{\mathit{2}}={\left(8\right)}^2+{\left(6\right)}^2 \\ \Rightarrow r^{\mathit{2}}=64+36=100 \end{gathered}$$

$\Rightarrow r=\sqrt{100}$ = 10 m

Thus, the radius of the new park is 10 m.

It is proposed to build a single 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 __10 m__.