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.
10​

Answer 1

GiveN :-

• Length of radius = 14 cm

• In 1 min minute hand swept 6° therefore in 5 min it swept 30°

To FinD :-

• Area swept by the minute hand in 5 minutes

SolutioN :-

$\large \longrightarrow \boxed{ \bf \blue{ Area = \pi {r}^{2} \times \frac{ \theta}{360}}} \\ \\\longrightarrow \sf Area =\frac{22}{7} \times 14 \times 14 \times \frac{30}{360} \\ \\\longrightarrow \sf Area =22 \times 7 \times \frac{1}{3} \\ \\ \longrightarrow \sf Area =\frac{154}{3} \\ \\\longrightarrow\boxed{ \sf \green{Area =51.3 \: {cm}^{2} }}$

Answer 2

Answer:

Minute hand completes full circle degree in one hour.

Swept by minute hand in 1 hour (ie 60 minutes) = 360°

Swept by Minutes hand in 1 minutes = 360/60 = 6°

Hence ø = 30° , r = 14cm

Area swept by Minutes hand = Area of sector

= ø/360 × πr²

= 30/360 × 22/7 × (14)²

= ½ × 22/7 × 14 × 14

= ½ × 22/1 × 2 × 14

= 154/3 cm²

Hence area swept by Minute hand in 5 minutes = 154/3 cm²