The area of the front face of the analog clock shown below is 50.24 square inches. The length of the minute hand is 0.25 inches less than the radius of the front face.
http://go.flvs.net/courses/1/flvs_57_3641_12676/ppg/respondus/pool_Geom_3641_0810_12/image0014e68c4f6.jpg
What is the length of the arc the minute hand makes when it moves from the number 3 to the number 7 on the clock?
Answer

1.31 inches

7.85 inches

8.37 inches

23.55 inches

Question

The area of the front face of the analog clock shown below is 50.24 square inches.  The length of the minute hand is 0.25 inches less than the radius of the front face.
http://go.flvs.net/courses/1/flvs_57_3641_12676/ppg/respondus/pool_Geom_3641_0810_12/image0014e68c4f6.jpg
What is the length of the arc the minute hand makes when it moves from the number 3 to the number 7 on the clock?
Answer
		
1.31 inches
		
7.85 inches
		
8.37 inches
		
23.55 inches

anonymous · Answer

Is it either 7.85 or 8.37?

anonymous · Answer

@hartnn can you help?

hartnn · Answer

from the area of the clock, you can find the radius of clock.

hartnn · Answer

could u find radius of clock ?

anonymous · Answer

i'm sorry, i'm really stuck

hartnn · Answer

that analog clock is a circular in shape.
and the area of circle is $A = \pi r^2$
here, A=50.24 is given, so first find what r =... ?

anonymous · Answer

i don't know what r is :(

hartnn · Answer

oh, r is simply the radius of the clock.

anonymous · Answer

okay how can i find the radius?

hartnn · Answer

50.24= $\pi r^2$
so, $r^2=$ 50.24/ $\pi$ 
so, r= $\sqrt{ 50.24/ \pi }$

hartnn · Answer

r=... ?

anonymous · Answer

50.24 divided by 3.14 = 16

hartnn · Answer

yup, and square root of 16 is =... ?

anonymous · Answer

4

hartnn · Answer

yes.The length of the minute hand is 0.25 inches less than the radius..
so, The length of the minute hand is 4-0.25 = ... ?

anonymous · Answer

3.75 :)

hartnn · Answer

correct. so your new radius r = 3.75
 now moving from 3 to 7(7-3=4), is as good as moving 1/3 rd of the circumference of the clock(4/12 = 1/12) , and the circumference is given by 2$\pi$r.
Hence , the required length of arc = 2$\pi$ r/3 = ... ?

hartnn · Answer

*4/12 = 1/3.

anonymous · Answer

uh i'm getting a little lost again, haha. can you break this part down for me

hartnn · Answer

sure, when the minute hand moves from 3 to 7, how much of the total circumference did it cover ?

hartnn · Answer

If it moves one full rotation from 12 to 12, it covers 1 entire circumference.

anonymous · Answer

um isn't it .25

hartnn · Answer

from 3 to 7 means 4 units.....
12 units = 1 circumference =  $2\pi r$
4 units = 1/3 circumference =  $2\pi r/3$
get this ?

anonymous · Answer

oh okay

hartnn · Answer

yeah, so u just need to find what $2 \pi r/3 = ...?$
when r=3.75

anonymous · Answer

2 times 3.14 times 3.75 divided by 3 is 7.85 inches :) thank you

hartnn · Answer

yup, thats correct :)
welcome ^_^