Question

The large hand of a clock is 42cm long. How many centimeters does its extremity move in20 minutes? (a) 80cm (b)88cm (c)18cm (d) 28cm​

Answer 1

Measurement of angles

We know that the minute hand rotates a full circle in 60 minutes. That is it does 360 degrees in 60 minutes or we can say that, In one rotation, a minute hand or large hand of a clock covers 360 degrees in 60 minutes. i.e. 360 degree = 60 minutes = 2π.

So, Angle traced out by the large hand or minute hand in 20 minutes is,

$\implies \dfrac{\cancel{360} \times 20}{\cancel{60}} \\ \\ \implies 6 \times 20 \\ \\ \implies 120^\circ$

Therefore, in 20 minutes it makes 120° = 2π/3.

Now we have the length of large hand of a clock and the length of large hand of a clock represents the radius of a circle.

The length of curve of angle θ and radius r is given by,

$\implies \boxed{\bf{l = r \theta}}$

where, l is the distance covered by the tip of a minute hand, θ is the angle in radian and r is the length or radius of the minute hand.

By substituting the known values in the formula, we get:

$\implies l = 42 \times \dfrac{2 \pi}{3} \\ \\ \implies l = \cancel{42} \times \dfrac{2 \times 22}{3 \times \cancel{ \: 7 \: }} \\ \\ \implies l = \cancel{ \: 6 \: } \times \dfrac{2 \times 22}{ \cancel{ \: 3 \: }} \\ \\ \implies l = 2 \times 2 \times 22 \\ \\ \implies \boxed{\bf{l = 88}}$

Hence, the distance moved by the extremely of the large hand is 88cm.

Answer 2

The Distance moved by the Minute Hand in 20 minutes is 88 cm.

Explanation

For the Explanation, refer the given attachment above.

Formula's used :

Length = radius * angle

⇒ l = rθ