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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