my college hive icon mycollegehive
Groups
My College Hive notifiction icon Questions
Tags
Quiz
Books
Given a circle of radius 9cm, and the length of the chord AB of a circle is 9√3 cm, find the area of the sector formed by arc AB.
CBSE class-10 math areas-related-to-circles
up
0
down

Given a circle of radius 9cm, and the length of the chord AB of a circle is 9√3 cm, find the area of the sector formed by arc AB.

27 views
Share Follow
james_mark
Asked by james_markrep:187
School not set Nigeria
31 July 2020

Comments





1 answer(s)

judziy
Judziy answeredrep:799
University of Benin Nigeria
01 August 2020
up
0
down

Length of cord = 2r sin(θ/2)

where r is the radius

9√3 = 2r sin(θ/2)

9√3 = 2(9) sin(θ/2)

9√3 = 18sin(θ/2)

divide both sides by 18

9√3 / 18 = sin(θ/2)

√3 / 2 = sin(θ/2)

θ/2 = sin-1(√3 / 2)

θ/2 = 60

multiply both sides by 2

θ = 120

Area of sector = 1/2 (Length of arc x radius)

Length of arc = θ/360 x 2πr

Area of sector = 1/2 (θ/360 x 2πr x r)

= θ/360 x πr2

where r is the radius

Area of sector  = 120/360 x π(9)2

= 27π

But π = 22/7

Area of sector = 27 x 22/7

= 84.85 cm2

Share
Comments






Your Answer

my college hive loader icon



Related Tags

CBSE

0 followers

56 questions

class-10

0 followers

56 questions

math

2 followers

985 questions