Question

The large hand of a clock is 42 cm long. How many centimetres does its extremity move in 20 minutes?

(A). \[2\pi \]cm
(B). \[28\pi \]cm
(C). \[8\pi \]cm
(D). None of these

Answer 1

Hint: We know that the minute hand rotates a full circle in 60 minutes. That is it does \[360{}^\circ \] in 60 minutes. Here the question is to calculate the distance travelled by the extremity of the minute hand(radius r of the circle) in 20 minutes. We can get this by using the arc length formula which is \[S=r\theta \]. Here S is the arc length, r is the radius of the circle and \[\theta \] is the central angle of the arc.

Complete step-by-step answer:

Angle rotated in 60 minutes = \[360{}^\circ \]

\[\theta \] = Angle rotated in 20 minutes
\[=\dfrac{360}{60}\times 20\]
\[=120{}^\circ \]
\[\theta =120{}^\circ \]
\[S=r\theta \] is the arc length formula of a circle
Putting \[\theta \] as \[\dfrac{2\pi }{3}\]and r as 42 cm we get
\[=\text{ }42\times \dfrac{2\pi }{3}\]
\[=28~\pi ~cm\]
Thus the extremity of the minute hand moves \[28~\pi ~cm\].


Note: We need to consider that the tip(which is extremity) of a minute hand in a clock travels a full 360deg in 60 minutes which is 1 hour. In order to calculate the distance travelled by the tip we need to find the distance travelled by the extremity in 20 minutes by using the formula for the arc length wherein we calculate the arc made by the minute hand in 20 minutes.