Ex 11.1 Q2 - Find the area of a quadrant of a circle whose circumference is 22 cm.
Solution:- Radius of the circle = r
Given,
Circumference = 22 cm
∴ 2πr = 22
∴ r =
22
/
2π
∴ r =
11
/
π
------- (i)*Since quadrant of a circus subtends 90° angle at the centre of the circle,
∴ 𝜃 = 90°
➙ We know that, area of a sector with angle '𝜃' and radius 'r' is given by,
𝜃
/
360°
× πr² ∴ Area of the quadrant
=
90°
/
360°
× π × (
11
/
π
)² = π ×
1
/
4
×
121
/
π × π
=
1
/
4
× 121 ×
7
/
22
=
77
/
8
cm²Alternatively,
*A quadrant of a circle means one of the four equal parts,
∴ Area of the quadrant
=
1
/
4
× Area of circle =
1
/
4
× πr² =
1
/
4
× π × (
11
/
π
)² = π ×
1
/
4
×
121
/
π × π
=
1
/
4
× 121 ×
7
/
22
=
77
/
8
cm²Hence,
The area of the quadrant is 77/8 cm².
------------------------------------
Try This..
✒ Given the circumference of a circle, find its area.
✒ If the radius of a circle is 7 cm, what is the area of one of its quadrants?
✒ Find the area of a semicircle whose diameter is 14 cm.
❌ Common Mistakes
Using the wrong value of π:▸ Stick to 22/7 unless instructed otherwise.Not dividing by 4 for a quadrant:▸ Many students forget this and give the full circle’s area.Rounding off too early:▸ Keep values exact until the final step to avoid silly errors.Mixing up formulas:▸ Remember, circumference = 2πr and area = πr².
📝 Related Questions:-
- Ex 11.1 Q1 - Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
- 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 Q2 Class 10
Class 10 Ex 11.1 Q2
Class 10 Chap 11 Ex 11.1 Q2
Class 10 Areas Related To Circles
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