Question

Find the area covered by minute hand of a clock from 12 to 3 if the radius of the clock is 14 cm​

Answer 1

Step-by-step explanation:

Minute hand completes 60 minutes in 1 full circle i.e. 360°

So, 60 mins = 360°

Therefore 1 min = 6°

From 12 to 3 means that the minute hand has covered 15 minutes , which becomes that the minute hand has covered 15x6° = 90°

Area of the sector formed =

$\frac{ \alpha }{360} \times \pi \times r {}^{2}$

where alpha= angle in degrees

Area= 154 cm²

$\frac{90}{360} \times \frac{22}{7} \times 14 \times 14$

Answer 2

Given,

The radius of the clock = 14 cm

Minute hand travels from 12 to 3

To find,

The area covered by the minute hand.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

From 12 to 3, it is a time span of 15 minutes.

Now,

The whole circular clock = 360°

And,

The whole circular clock = 60minutes

Thus,

60 minutes of time span = 360°

1 minute of time span = 360°/60

15 minutes of time span = (360° × 15)/60 = 90°

So, the angular displacement of the minute hand = 90°

Now, we know that 90° angle is subtended by a quadrant (¼th part) of a circle.

So, we need to find out the area of a quadrant of the clock's circle, to calculate the area covered by the minute hand.

Thus,

Area covered by the minute hand = ¼ × (22/7) × (14)² = 154 cm²

Hence, the area covered by the minute hand is 154 cm².