# 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 ______. - Mathematics

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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

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

∴ Radius R1 of first circular park = 8 m

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

∴ Radius R2 of second circular park = 6 m

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 10 m.

Concept: Area of Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.1 | Q 6 | Page 121

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