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 ______.

#### Options

10 m

15 m

20 m

24 m

#### Solution

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 **10 m**.

**Explanation:**

Let D_{1} be the diameter of the first circular park = 16 m

∴ Radius R_{1} of first circular park = 8 m

Let D_{2} be the diameter of the second circular park = 12 m

∴ Radius R_{2} of second circular park = 6 m

Area of first circular park = πr^{2} = π(8)^{2} = 64 π m^{2}

Area of second circular park = πr^{2} = π(6)^{2} = 36 π m^{2}

Now, we are given that,

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

∴ πR^{2} = 64 π + 36π = 100π ......(Where R is the radius of the single circular park)

πR^{2} = 100π

⇒ R^{2} = 100

⇒ R = 10

∴ Radius of the single circular park will be 10 m.