major segment of a circle

Question

The radius of a circle is 5cm.Achord of length square root 50 cm is drawn in the circle.Find the area of the major segment?

Answer 1

Given : The radius of the circle (r ) = 5 cm.

And, the length of the chord = √50 cm.

Area of major segment = Area of circle - Area of minor segment.

Area of minor segment = Area of the sector - Area of .

The area of the sector = .

Here ,, in .

So, .

Substitute the values , , and r = 5 in .

Area of the sector = 

                           =

                           = .

Now, Area of = .

Base = Height = Radius of the circle = 5 cm.

Substitute the values of base = 5, and height = 5 in .

50−−√

Answer 2

Area of =

                         = .

Area of minor segment = Area of the sector - Area of .

                                     =

                                     = .

 

50−−√

Answer 3

Area of major segment = Area of circle - Area of minor segment.

                                     =

                                      = .

Therefore, area of the major segment is .50−−√50−−√50−−√50−−√

Answer 4

There are two main "slices" of a circle

The "pizza" slice is called a Sector.

And the slice made by a chord is called a Segment.

  and

(b) Area of segment when height and length of the chord of the segment are given:
Let r =  radius of the circle
h =  height of the segment
c =  length of the chord.

We note that ODB is a right triangle; the hypotenuse is OB = r and the other two sides are OD = r - h and BD = c/2.

By Pythagorean Theorem

Solving for r, c and h, we obtain the following formulas

--- (1)

--- (2)

--- (3)

Note:

Gives the height of the major segment h = .

Gives the height of the minor segment h =

Many formulas are given for finding the approximate area of a segment.

Two of the common methods are:

Method-I:

Note: If the height of the segment is less of radius of the circle, then .

Method-II:

The radius of a circle is 5cm and a chord of length square root 50 cm.

The height of the major sigment is h = .

h = 5 + sqrt [(25 - (50/4)]

h = 5 + sqrt [150/4]

h = 5 + sqrt [37.5]

h = 5 +6 = 11 cm

.

A = (11 / 6√50) [(3(121)+4(50)]

A = (11 / 42) [363+400]

A = (11 / 42) [763]

A = (11 / 42) [763]

A = 200 cm².

Comments

Sorry ! typo mistake.

The height of the major sigment is h = .

h = 5 + sqrt [(25 - (50/4)]

h = 5 + sqrt [12.4]

h = 5 + 3.54

h = 8.54 cm

.

A = (8.54 / 6√50) [3(72.9316) + 4(50)]

A = (8.54 / 42.43) [418.7948]

A = (0.201) [418.7948]

A = 84.25 cm².