Ex 11.1, 6 - Chapter 11 Class 10 Areas related to Circles

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 11.1, 6
A chord of a circle of radius 15 cm subtends an angle of 60Β° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use Ο = 3.14 and β3 = 1.73)
In a given circle,
Radius (r) = 15 cm
And, π½ = 60Β°
Now,
Area of segment APB = Area of sector OAPB β Area of ΞOAB
Finding Area of sector OAPB
Area of sector OAPB = π/360 Γ ππ2
= 60/360 Γ 3.14 Γ (15)2
= 1/6 Γ 3.14 Γ 15 Γ 15
= 1/2 Γ 3.14 Γ 5 Γ 15
= 117.75 cm2
Finding area of Ξ AOB
We draw OM β₯ AB
β΄ β OMB = β OMA = 90Β°
And, by symmetry
M is the mid-point of AB
β΄ BM = AM = 1/2 AB
In right triangle Ξ OMA
sin O = (side opposite to angle O)/Hypotenuse
sin ππΒ° = ππ΄/π¨πΆ
1/2=π΄π/15
15/2 = AM
AM = ππ/π
In right triangle Ξ OMA
cos O = (π πππ ππππππππ‘ π‘π πππππ π)/π»π¦πππ‘πππ’π π
cos ππΒ° = πΆπ΄/π¨πΆ
β3/2=ππ/21
β3/2 Γ 15 = OM
OM = βπ/π Γ 15
From (1)
AM = π/πAB
2AM = AB
AB = 2AM
Putting value of AM
AB = 2 Γ 1/2 Γ 15
AB = 15 cm
Now,
Area of Ξ AOB = 1/2 Γ Base Γ Height
= π/π Γ AB Γ OM
= 1/2 Γ 15 Γ β3/2 Γ 15
= 1/2 Γ 15 Γ 1.73/2 Γ 15
= 97.3125 cm2
Therefore,
Area of segment APB
= Area of sector OAPB β Area of ΞOAB
= 117.75 β 97.3125
= 20.4375 cm2
Thus, Area of minor segment = 20.4375 cm2
Now,
Area of major segment = Area of circle β Area of minor segment
= Οr2β 20.4375
= 3.14 Γ πππβ 20.4375
= 3.14 Γ 15 Γ 15β"20.4375"
= 706.5 β 20.4375
= 686.0625 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!