we know that
The clock represent a complete circle
The circumference of a circle is giving by the formula
C=2pi r
where
r is the radius of the circle
In this problem
The radius of the circle is equal to the length of the minute hand
so
r=6 in
C=2pi(6)
C=12pi in
The length of the complete circle subtends a central angle 0f 360 degrees
Find out what is the central angle for 10 minutes (6:35 to 6:45)
we know that
6 hours represent 90 degrees
so
1 hour represent 15 degrees
1 hour represent 60 minutes so
divide by 6
15/6=2.5 degrees
therefore
using proportion
12pi/360=x/2.5
solve for x
x=12pi(2.5)/360
use 3.14 as pi
x=12(3.14)(2.5)/360
x=0.26 inches
The answer is 0.26 inches