Q: Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. (Use $\pi = \frac{22}{7}$)

Given:\nRadius of the circle ($r$) = 6 cm\nAngle of the sector ($\theta$) = 60° \nFormula for the area of a sector:\nArea = $\frac{\theta}{360°} \times \pi r^2$ \nSubstituting the given values:\nArea = $\frac{60°}{360°} \times \frac{22}{7} \times (6)^2$\nArea = $\frac{1}{6} \times \frac{22}{7} \time

Q: Find the area of a quadrant of a circle whose circumference is 22 cm. (Use $\pi = \frac{22}{7}$)

Given:\nCircumference ($C$) = 22 cm \nStep 1: Find the radius ($r$) of the circle using the circumference formula. $C = 2\pi r$ $22 = 2 \times \frac{22}{7} \times r$ $22 = \frac{44}{7} \times r$ $r = \frac{22 \times 7}{44}$ $r = \frac{7}{2} \text{ cm} = 3.5 \text{ cm}$ \nStep 2: Find the area of the

Q: The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. (Use $\pi = \frac{22}{7}$)

Given:\nRadius of the circular region ($r$) = Length of minute hand = 14 cm \nStep 1: Find the angle swept by the minute hand in 1 minute.\nA minute hand completes a full rotation ($360^{\circ}$) in 60 minutes.\nAngle swept in 1 minute = $\frac{360^{\circ}}{60} = 6^{\circ}$ \nStep 2: Find the angle

Q: A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment. (Use $\pi = 3.14$)

Given:\nRadius ($r$) = 10 cm\nCentral angle ($\theta$) = 90° \nStep 1: Find the area of the corresponding sector.\nArea of sector = $\frac{\theta}{360^{\circ}} \times \pi r^2$\nArea of sector = $\frac{90^{\circ}}{360^{\circ}} \times 3.14 \times (10)^2$\nArea of sector = $\frac{1}{4} \times 3.14 \tim

Question 1

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. (Use $\pi = \frac{22}{7}$)

Accepted Answer

Given:
Radius of the circle ($r$) = 6 cm
Angle of the sector ($	heta$) = 60° 
Formula for the area of a sector:
Area = $\frac{	heta}{360°} 	imes \pi r^2$ 
Substituting the given values:
Area = $\frac{60°}{360°} 	imes \frac{22}{7} 	imes (6)^2$
Area = $\frac{1}{6} 	imes \frac{22}{7} 	ime

Question 2

Find the area of a quadrant of a circle whose circumference is 22 cm. (Use $\pi = \frac{22}{7}$)

Accepted Answer

Given:
Circumference ($C$) = 22 cm 
Step 1: Find the radius ($r$) of the circle using the circumference formula. $C = 2\pi r$ $22 = 2 	imes \frac{22}{7} 	imes r$ $22 = \frac{44}{7} 	imes r$ $r = \frac{22 	imes 7}{44}$ $r = \frac{7}{2} 	ext{ cm} = 3.5 	ext{ cm}$ 
Step 2: Find the area of the

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. (Use $\pi = \frac{22}{7}$)

Accepted Answer

Given:
Radius of the circular region ($r$) = Length of minute hand = 14 cm 
Step 1: Find the angle swept by the minute hand in 1 minute.
A minute hand completes a full rotation ($360^{\circ}$) in 60 minutes.
Angle swept in 1 minute = $\frac{360^{\circ}}{60} = 6^{\circ}$ 
Step 2: Find the angle

Question 4

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment. (Use $\pi = 3.14$)

Accepted Answer

Given:
Radius ($r$) = 10 cm
Central angle ($	heta$) = 90° 
Step 1: Find the area of the corresponding sector.
Area of sector = $\frac{	heta}{360^{\circ}} 	imes \pi r^2$
Area of sector = $\frac{90^{\circ}}{360^{\circ}} 	imes 3.14 	imes (10)^2$
Area of sector = $\frac{1}{4} 	imes 3.14 	im

Areas Related to Circles