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.
Solution:- The minute hand completes one rotation in 1 hour or 60 minutes.
Therefore,
*Angle swept by minute hand in 60
minutes = 360°
∴ Angle swept by minute hand in 1
minute =
360°
/
60
= 6° ∴ Angle swept by minute hand in 5
minutes = 6° × 5 = 30°
Now,
Angle = 𝜃 = 30°
Radius = r = 14 cm
➙ The area swept by minute hand in 5 minutes
= Area of a sector with radius 14 cm and angle 30°
*Area of a sector with radius 'r' and angle '𝜃' is given by,
𝜃
/
360°
× πr² =
30°
/
360°
×
22
/
7
× (14)² =
1
/
12
×
22
/
7
× 196 =
22 × 196
/
12 × 7
=
154
/
3
cm²Hence,
The area swept by the minute hand in 5 minutes is 154/3 cm².
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Try This..
✒ The minute hand of a clock is 21 cm. Find the area swept in 15 minutes.
✒ A wheel of radius 7 cm rotates through 90°. Find the area covered.
✒ What is the area swept by the minute hand in 10 minutes if its length is 10 cm?
❌ Common Mistakes
Forget to convert minutes to degrees:▸ Always remember: 1 minute = 6 degreesUse wrong radius:▸ The radius is the length of the minute hand, not the circumference!Make calculation errors with π:▸ Use 22/7 or 3.14 consistently throughout the question.Misunderstand what “area swept” means:▸ It refers to the sector of the circle, not the arc length.
📝 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 Q2 - Find the area of a quadrant of a circle whose circumference is 22 cm.
- 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)
Queries Solved:-
Class 10 Ex 11.1
Ex 11.1 Q3 Class 10
Class 10 Ex 11.1 Q3
Class 10 Chap 11 Ex 11.1 Q3
Class 10 Areas Related To Circles
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