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Answers
Given:-
The minute hand of a clock is 21 cm long.
To find:-
★ Distance traveled by clock tip in 20 minutes.
★ Area swept by clock in 20 minutes.
⠀
Formula used:-
✯ Area of arc
⠀⠀⠀= Angle of arc in radian/2π × Area of
⠀⠀⠀⠀circle
⠀
✯ Length of arc
⠀⠀⠀=Angle of arc in radian/2π ×
⠀⠀⠀⠀perimeter of circle
⠀
⠀
★ The minute hand of a clock is 21 cm long.
★ So radius of circle = 21 cm.
★ Angle covered by clock in 60 minute
= 360°
⠀
★ So Angle covered by clock in 20 minute
= 360° × 20/60 = 120°
★ This shoes that the minute hand can move 120° arc
⠀
⠀
✯ Area of arc
⠀⠀⠀= Angle of arc in Radian/2π × Area
⠀⠀⠀⠀ of circle
⠀
✯ Area of arc
⠀⠀⠀= Angle of arc in Radian/2π × Area
⠀⠀⠀⠀ of circle × π × (radius)^2
⠀⠀⠀= 2π/3 / 2π × π × (21)^2
⠀
⠀
★Area of arc=461.81 cm².
⠀
⠀
✯ Length of arc
⠀⠀⠀= Angle of arc in radian/2π × ⠀⠀⠀⠀Perimeter of circle
⠀⠀
✯ Length of arc
⠀⠀⠀= Angle of arc in radian/2π × 2 × π × ⠀⠀⠀⠀(radius)^2
⠀
⠀⠀⠀= 2π/3 / 2π × 2 × π × 21
⠀
★Length of arc=43.98 cm.
⟶Therefore, the distance traveled by clock tip in 20 minutes is 43.98 cm and area swept by clock in 20 minutes is 461.81 cm².