The short hand and long hand clock are 4cmand6cm long respectively find the distance traveled by their tips in two days?

Every day, the hour hand makes 2 complete revolutions and the minute hand makes 24 revolutions (one per hour). So we have 4 complete revolutions on the hour hand and 48 on the minute hand.

First, let us find out the distance per revolution these make. If you noticed on a clock, these would be considered radii, the minute hand makes:

C = 2πr

==> C = 2π(4)

==> C = 8π

==> C ≈ 25.133 cm/revolution

and the hour hand makes:

C = 2πr

==> C = 2π(6)

==> C = 12π

==> C ≈ 37.699 cm/revolution

So the sums are:

48(8π cm) + 4(12π cm)

= 384π cm + 48π cm

= 432π cm

≈ 1,357.168 cm

Therefore, the sum of the distances traveled is about 1,357 cm.