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. 15 m C. 20 m D. 24 m

Answer 1

A. 10 m

Let D₁ be the diameter of the first circular park = 16m

∴ Radius R₁ of first circular park = 8m

Let D₂ be the diameter of the second circular park = 12m

∴ Radius R₂ of second circular park = 6m

Area of first circular park = πr² = π(8)² = 64 π m²

Area of second circular park = πr² = π(6)² = 36 π m²

Now, we are given that,

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

∴ πR² = 64 π + 36π = 100π

(where R is the radius of the single circular park)

πR² = 100π ⇒ R² = 100 ⇒ R = 10

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