The area swept by the minute hand in 12 minutes is 181.58 cm²
Step-by-step explanation:
In the circle clock
- The circumference of the circle is divided into 12 equal arcs
- The central angle of each arc is 30°, because the measure of the circle is 360° and divided by 12
- The central angle between each two consecutive hours is 30°
- There are 5 minutes between each two consecutive hours, then the central angle between each two consecutive minutes is 6° because 30° ÷ 5 = 6°
- When the minute hand is moved than the radius of the circle is the length of the minute hand
- When the hour hand is moved than the radius of the circle is the length of the hour hand
∵ The minute hand is swept by 12 minutes
∵ The central angle between each two consecutive minutes = 6°
∴ The central angle when the minute hand swept 12 minutes =
6 × 12 = 72°
∵ The area of a sector of a circle = ,
where r is the radius of the circle and x is the central angle of
the sector
∵ The radius of the circle is the length of the minute hand
∵ The minute hand in a clock is 17 cm long
∴ r = 17 cm
∵ The measure of the central angle is 72°
∴ x = 72°
- Substitute these values in the rule of the area of a sector
∵ Area =
∴ Area = 181.58 cm²
The area swept by the minute hand in 12 minutes is 181.58 cm²
Learn more:
You can learn more about the area of the sector in brainly.com/question/3456442
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