Math # If a length of a minute hand clock is 1.5 cm,how far it go in 40 minutes​

6.28cm

We are given that the minute hand of a clock is 1.5 cm long.

We need to find the distance covered by its tip in 40 minutes. Its tip is obviously the last point on the hand which moves in a circular motion. Hence, it will cover the perimeter. So, we basically need to find that part of circumference, which can cover in 40 minutes.

We know that Circumference=2πr, where r is the radius of the circle. So, when we cover 2π=360∘, we get Circumference=2πr.

Hence, r is multiplied to the angle covered.

Hence, now we have: l=r.θ

, where l is the arc length, r is the radius that is the length of the minute hand and θ is the angle covered.

Now, we know about the formula a bit more.

We also know that 1 hr = 60 minutes.

Hence, a minute hand will cover the whole 360∘

in 60 minutes.

So, 60 minutes are equivalent to 360∘

.

⇒ 1 minute is equivalent to 360∘60=6∘.

⇒ 40 minutes are equivalent to 40×6∘=240∘.

Now, we need the angle in radians.

180∘=π

⇒1∘=π180

⇒240∘=π180×240=4π3 ……….(1)

Now, coming to the formula l=r.θ

.

⇒l=(1.5)×4π3 (Using (1))

⇒l=(1.5)×4×3.143=6.28cm (Since, π=3.14)

Hence, l=6.28cm is the distance covered by its tip in 40 minutes.

286 