Ex 11.1 Q1 - Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Solution:- OACB be a sector of the circle making 60° angle at centre 'O' of the circle.
Given,
Radius = r = 6 cm
Angle = 𝜃 = 60°
➙ We know that, area of a sector with angle '𝜃' and radius 'r' is given by,
𝜃
/
360°
× πr² ∴ Area of sector OACB
=
60°
/
360°
×
22
/
7
× (6)² =
1
/
6
×
22
/
7
× 36 =
22 × 6
/
7
=
132
/
7
cm²Hence,
The area of the sector is 132/7 cm².
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Try This..
✒ If the area of a sector is 25 cm² and the angle is 60°, find the radius.
✒ Calculate the area of a semicircle with a radius of 8 cm.
✒ A circular pizza has a radius of 10 cm. What is the area of a slice with a 120° angle?
✒ Find the area of a sector with radius 7 cm and angle 90°.
❌ Common Mistakes
Wrong Angle Units:▸ Always check that the angle is in degrees (not radians).Incorrect Radius Squaring:▸ Don’t forget to square the radius: means r × r.Using the Wrong Formula:▸ Don’t confuse the area of a sector with the length of an arc.Calculation Errors:▸ Always double-check your multiplication and division.
📝 Related Questions:-
- Ex 11.1 Q2 - Find the area of a quadrant of a circle whose circumference is 22 cm.
- Ex 11.1 Q3 - The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
- 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)
- Ex 11.1 Q12 - To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)
Queries Solved:-
Class 10 Ex 11.1
Ex 11.1 Q1 Class 10
Class 10 Ex 11.1 Q1
Class 10 Chap 11 Ex 11.1 Q1
Class 10 Areas Related To Circles
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