Ex 11.1 Q4 - A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (ii) major sector. (Use π = 3.14)
Solution:-Given,
Radius = r = 10 cm
Angle = 𝜃 = 90°
Let,
AB be the chord which subtends a right angle at centre 'O' of the circle.
Quick Recap:
Minor segment: The smaller region of the circle formed by a chord and the arc it intercepts.
Major sector: The larger region enclosed by two radii and the arc between them.
( i ) Area of Minor Segment:
*Area of Minor Sector OACB
=
𝜃
/
360°
× πr² =
90°
/
360°
× 3.14 × (10)² =
1
/
4
× 3.14 × 100 =
314
/
4
= 78.5 cm²
*Area of ∆AOB
=
1
/
2
× Base × Height =
1
/
2
× OA × OB =
1
/
2
× 10 × 10 =
100
/
2
= 50 cm²
∴ Area of Minor Segment ACB
= Area of Minor - Area of ∆AOB
Sector OACB
= 78.5 - 50
= 28.5 cm²
Therefore, Area of Minor Segment is 28.5 cm².
( ii ) Area of Major Sector:
*Area of Major Sector OADB
=
360° - 𝜃
/
360°
× πr² =
360° - 90°
/
360°
× 3.14 × (10)² =
270°
/
360°
× 3.14 × 100 =
3
/
4
× 314 =
942
/
4
= 235.5 cm²
Alternatively..
*Area of Major Sector OADB
= πr² - Area of Minor Sector OACB
= 3.14 × (10)² - 78.5
= 3.14 × 100 - 78.5
= 314 - 78.5
= 235.5 cm²
Therefore, Area of Major Sector is 235.5 cm².
Hence,
The area of Minor Segment and Major Sector is 28.5 cm² and 235.5 cm² respectively.
------------------------------------
Try This..
✒ A circular pizza has a radius of 12 cm. If a slice makes a 120° angle at the centre, find the area of the slice.
✒ A wheel makes 500 revolutions in moving 1.1 km. Find the radius of the wheel.
✒ A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the area of the corresponding minor segment.
✒ The minute hand of a clock is 10 cm long. Find the area swept by the minute hand in 30 minutes.
❌ Common Mistakes
Using the wrong formula:▸ Many students confuse sector and segment formulas. Always subtract the triangle’s area for a segment!Incorrect angle conversion:▸ Ensure you’re using degrees (not radians) unless specified.Skipping steps:▸ Missing out on calculating triangle area will lead to the wrong answer for the segment.Not using the given π value:▸ Always use π = 3.14 if it's mentioned in the question.
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 11.1
Ex 11.1 Q4 Class 10
Class 10 Ex 11.1 Q4
Class 10 Chap 11 Ex 11.1 Q4
Class 10 Areas Related To Circles
If you found it helpful, please leave a comment below sharing your thoughts or questions.
Don’t forget to share it with your classmates to help them learn too.
Good luck, and happy learning!
Together, let’s make math simpler and more enjoyable for everyone!