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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

a. 10 m

b. 15 m

c. 20 m

d. 14 m

**Solution:**

Given, a single circular park equal in area to the sum of two circular parks of diameters 16 m and 12 m

We have to find the radius of the new park.

__Area of circle__ = πr²

Where r is the radius

Diameter of circular park D₁ = 16 m

So, radius r₁ = 8 m

Area of circle with radius 8 m = π(8)²

= 64π

__Diameter__ of circular park D₂ = 12 m

So, radius r₂ = 6 m

Area of circle with radius 6 m = π(6)²

= 36π

Sum of the areas of two parks with diameters 16 m and 12 m = 64π + 36π

= 100π

Let the radius of new park be R

Area of new park = πR²

Given, 100π = πR²

R² = 100

Taking square root,

R = 10 m

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

**✦ Try This:** It is proposed to build a single square park equal in area to the sum of areas of two square parks of side lengths 6 m and 2 m in a locality. The side length of the new park would be

Given, side lengths of two square parks are 6 m and 2 m.

New park is equal in area to the sum of the areas of two squares.

We have to find the side length of the new park.

Area of square = a²

Area of square with side 6 m = (6)² = 36 m²

Area of square with side 2 m = (2)² = 4 m²

Sum of the area of two parks = 36 + 4 = 40

Let the side length of the new park be A

Area of new park = A²

Given, A² = 40

Taking __square root__,

A = 2√10 m

Therefore, the side length of the new park is 2√10 m.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 6**

## 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. 14 m

**Summary:**

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

**☛ Related Questions:**

- The area of the circle that can be inscribed in a square of side 6 cm is a. 36π cm², b. 18π cm², c. . . . .
- The area of the square that can be inscribed in a circle of radius 8 cm is a. 256 cm², b. 128 cm², c . . . .
- The radius of a circle whose circumference is equal to the sum of the circumferences of the two circ . . . .

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