AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

What will be the lengths of the arcs and area of the minor segment cut off from a circle of radius 12 cm by a chord 12cm long?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

62.85 c m 2

13.05 c m 2

62.85 c m 2

13.07 c m 2

62.80 c m 2

13.07 c m 2

62.85 c m 2

13.75 c m 2

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We have to find the lengths of the arcs and area of the minor segment cut off from a circle of radius 12 cm by a chord 12cm long.
Value of

π = 227

Area of the minor segment =

π r 2 × θ 360 ° − 12 × r 2 × sin θ

,
Where, r is the radius.
Calculating the area of the minor segment,
Question Image

Suppose AB is the chord.
Joining A and B to O, we get an equilateral triangle OAB.
Area of the sector

= π r 2 × θ 360 °

Where, ‘

θ

’ is the angle of the sector and r is the radius.
Note that the angles are equal since,

θ = 60 °

= θ 3600 × π r 2 − 12 × r 2 × sin θ = 6003600 × π 122 − 12 × 122 × sin 600 = 1600 × 227 × 144 − 12 × 144 × 32 = 13.07

Calculating the length of the arc cut off from the circle,
Length of the arc is

= 2 π r × θ 360 °

Note that,
Length of arc=

2 π r − 2 π r θ 3600

Put

π = 227

and r=12cm So, length of the larger arc=

2 π r (1 − θ 3600)

= 2 × 227 × 12 × 56

=62.85 cm2
So, the length of the arc cut off from circle is

62.85 c m 2

and the area of the minor segment is

13.07 c m 2

.
Therefore, option 2 is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!