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

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 swept in 5 minutes ($\theta$). $\theta = 5 \times 6^{\circ} = 30^{\circ}$ \nStep 3: Calculate the area of the sector swept in 5 minutes.\nArea = $\frac{\theta}{360^{\circ}} \times \pi r^2$\nArea = $\frac{30^{\circ}}{360^{\circ}} \times \frac{22}{7} \times (14)^2$\nArea = $\frac{1}{12} \times \frac{22}{7} \times 14 \times 14$\nArea = $\frac{1}{12} \times 22 \times 2 \times 14$\nArea = $\frac{1}{6} \times 22 \times 14$\nArea = $\frac{11 \times 14}{3}$\nArea = $\frac{154}{3} \text{ cm}^2 = 51.33 \text{ cm}^2$ \nTherefore, the area swept by the minute hand in 5 minutes is $\frac{154}{3} \text{ cm}^2$.

Question

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 swept in 5 minutes ($	heta$). $	heta = 5 	imes 6^{\circ} = 30^{\circ}$ 
Step 3: Calculate the area of the sector swept in 5 minutes.
Area = $\frac{	heta}{360^{\circ}} 	imes \pi r^2$
Area = $\frac{30^{\circ}}{360^{\circ}} 	imes \frac{22}{7} 	imes (14)^2$
Area = $\frac{1}{12} 	imes \frac{22}{7} 	imes 14 	imes 14$
Area = $\frac{1}{12} 	imes 22 	imes 2 	imes 14$
Area = $\frac{1}{6} 	imes 22 	imes 14$
Area = $\frac{11 	imes 14}{3}$
Area = $\frac{154}{3} 	ext{ cm}^2 = 51.33 	ext{ cm}^2$ 
Therefore, the area swept by the minute hand in 5 minutes is $\frac{154}{3} 	ext{ cm}^2$.

CBSE · Class 10 · Mathematics · Areas Related to CirclesThe length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. (Use $\pi = \frac{22}{7}$)