Question

4. The short and long hand of a clock are 4 cm and 6 cm respectively. Find the sum of
distances travelled by their tips in one day.​

Answer 1

Answer:

955.56cm

Step-by-step explanation:

for caluclating distance of a tip of hand we first caluclate the circumferance which the distance travelled by tip of the hand.

first consider the long hand:r=6

$circumference(c) = 2\pi \: r$

c = 2(3.14)(6)

c = 37.68cm

we know that long hand in minute hand so it travels 24 circles in one day .

.therfore total distance travelled in one day by lang hand=

24 (37.68)=905.32cm...eq1

similarly small hands circumference =

2 (3.14)(4) =25.12cm

we know that small hand is hour hand so it travels only 2 circles in one day

so distance coverd by small hand in one day = 2 (25.12)=50.24cm.......eq2

total distance coverd by both small and long hand = eq1+eq2

=905.32+50.24

=955.56cm

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.