Exercise 12.2
Question 1:
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Let OACB be a sector of the circle making 60° angle at centre O of the circle.
Area of sector of angle θ =
Area of sector OACB =
Therefore, the area of the sector of the circle making 60° at the centre of the circle is
Question 2:
Find the area of a quadrant of a circle whose circumference is 22 cm.
Let the radius of the circle be r.
Circumference = 22 cm
2πr = 22
Quadrant of circle will subtend 90° angle at the centre of the circle.
Area of such quadrant of the circle
Question 3:
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
We know that in 1 hour (i.e., 60 minutes), the minute hand rotates 360°.
In 5 minutes, minute hand will rotate =
Therefore, the area swept by the minute hand in 5 minutes will be the area of a sector of 30° in a circle of 14 cm radius.
Area of sector of angle θ =
Area of sector of 30°
Therefore, the area swept by the minute hand in 5 minutes is
