Quadratic Equations

Quadratic Equations Class X Exercise 4.3

Exercise 4.4

Areas Related to Circles

12. Areas Related to Circles

Circle

The collection of points which is located at a certain distance from a certain point is said to be circle.

The certain distance is known as radius of the circle.

The certain point is known as centre of the circle.

The collection of points is known as circumference of the circle.

It is a geometrical figure in which infinite sides.

Area

The region which is surrounded by a closed geometrical figure is said to be area.

Calculation of area of a circle

When circle is divided into 16 equal parts from the centre of the circle. It is converted into a rectangle of length πr and breadth of r.

Important formulae of the circle

Area of cirle = πr²

Circumference of the circle = 2πr

Area of sector of a circle = πr²θ/360⁰

Area of minor segment = πr²2θ/360⁰ - r²sin2θ/2

Exercise 12.1

1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Solution:

Let the radius of the circle be R.

We know that

Circumference of the circle = C = 2πr

From question it is clear that

r₁ = 19 cm

r₂ = 9 cm

R = ?

Therefore,

C = C₁ + C₂

Therefore,

R = 2π(r₁ + r₂)/2π

Therefore,

R = 19 + 9

R = 28 cm Ans.

2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Solution

Let the radius be r.

From question it is clear that

r =?

r₁ = 8 cm

r₂ = 6 cm

Therefore,

Radius of the circle = r² = π(r₁² + r₂²)/π

r² = 8² + 6²

r² = 64 + 36

r² = 100

r = 10 cm. Ans.