Math, asked by kriya16, 2 months ago

Which of these is equivalent to the sum of the lengths of arc corresponding to the minor and major segment of a circle of radius 12 cm?​

Answers

Answered by Kaushalsingh74883508
2

Step-by-step explanation:

given a circle of radius 12 cm.

OA=OB=12 cm= radius of the circle and .Let AB be the chord of 12 cm. hence we get an equilateral triangle OAB inside the circle that means ∠O=∠A=∠B=60

o

to find the length of the arcs (APB and ADB) of circle.

circumference of the circle =2πr=2π×12 length of the arc APB of the circle =

360

2π×12×60

=

360

2π×12×60

=4π=12.56 cm

Now the length of the arc AQB=

360

2π×12×(360−60)

=

360

2π×12×300

=20π

=62.80 cm

Now to find the Area of the minor segment

= Area of the sector ABCA= Area of the sector AOBCA

= Area of the triangle OAB

Area of the sector AOBCA=π×(12)

2

×

360

60

=π×12×2=24π=75.36 cm

2

Area of the triangle OAB =

4

3

×12×12=36

3

=62.28 cm

2

hence area of the minor segment is =(75.36−62.28) cm

2

=13.08 cm

2

Answered by amitnrw
0

Given : a circle of radius 12 cm​

To find : sum of lengths of arcs corresponding to minor and major segment of  the circle

solution:

sum of lengths of arcs corresponding to minor and major segment of  the circle  = circumference of the circle

circumference of a circle = 2 π R

R = Radius = 12 cm

=> circumference of the circle = 2 π ( 12)

= 24 π  cm

≈ 75.4 cm

sum of lengths of arcs corresponding to minor and major segment of  the circle of radius 12 cm​  is  about 75.4 cm

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