Question

The diameter of a clock's face is 6 inches. Find the length of the mirror arc formed by the hands of the clock at 4:00. Round to the nearest hundredth.

Answer 1

we know that

360°/12 hour-----------> 30°/hour

Central angle at 4 .00 is 120 degrees

the radius of a clock is 6/2-----> r=3 in
length of a circumference=2*pi*r-----> 2*pi*3----> 18.84 in

the minor arc at 4 .00 is for a central angle of 120°
so
if 360° (full circle)---------> has a length of 18.84 in
120°----------------------> X
X=120*18.84/360-------> X=6.28 in

the answer is
6.28 in