Question

The long and the short hand of a clock are 6 cmand 4 cm long respectively. Find the sum of the distance travelled by the tips in 24 hours

Answer 1

Let the radius of the long hand be R and the short hand be r.
R=6 cm
r=4 cm
we know that the long hand fully rotate only 2 in 24 hours.
So, distanc travelledby it in 2 rotetion=
(distance travelled by it in 1 rotatetion)×2
=[(2πR)×2] cm
=[2×π×6×2] cm
=24π cm
we also know that the short hand fully rotate only 24 in 24 hours.
So, distanc travelledby it in 24 rotetion=
(distance travelled by it in 1 rotatetion)×24
=[(2πr)×24] cm
=[2×π×4×24] cm
=192π cm
So,the sum of the distance travelled by the tips in 24 hours =[24π+192π] cm = 216π cm

Answer 2

Answer:

Given :

Length of short hand = 4 cm

Length of long hand = 6 cm

We know short hand make 1 revolution in 12 hours while long hand in 1 hour.

Distance travelled by short hand in 24 hours = 2 × 2 π × 4 = 16 π cm

Distance travelled by long hand in 24 hours = 24 × 2 π × 6 = 288 π cm

Total distance travelled = 16 π cm +  288 π cm = 304 π cm

Therefore ,  sum of distances travelled by their tips in one day is 304 π cm.