The area of the front face of the analog clock shown below is 153.86 square inches. The length of the minute hand is 0.2 inches less than the radius of the front face.

What is the length of the arc, rounded to the nearest hundredth of an inch, the minute hand makes when it moves from the number 8 to the number 2 on the clock?

Question

The area of the front face of the analog clock shown below is 153.86 square inches.  The length of the minute hand is 0.2 inches less than the radius of the front face.
 
What is the length of the arc, rounded to the nearest hundredth of an inch, the minute hand makes when it moves from the number 8 to the number 2 on the clock?

anonymous · Answer

PLS HELP

campbell_st · Answer

find the radius of the clock face

$$153. 86 = \pi r^2$$

$$r = \sqrt{\frac{153.86}{\pi}}$$

next subtract 0.2 inches from the radius to get the length of the minute hand

the minute has will move through 180 degrees or pi radians if it moves from 8 to 2

the arc length will be half the circumference of the circle with radius of the minute hand