Find the arc length of the 8 inch hand of a clock that sweeps a 5 hour arc. Round to the nearest 10th of an inch.

Question

For a math quiz. Please help.

Answer 1

circumference=2πr

r=8 in

c=2∗(3.14)∗8

c=50.24 in

5 hours/24 hours=.208

50.24∗.208=10.4

arc length =10.4 inches

Answer 2

Hi Emma,

If the hour-hand is 8 inches long, that would be the radius in your arc length formula.

 

A 5-hour arc is a little harder, but think of the clock face as being divided into 12 small arcs.   

 

The arc length can be calculated using proportions:

 

    5 small arcs (hours)             arc length of a 5-hour arc

---------------------- =    ------------------------

12 small arcs (total)                  total length around the face of the clock

 

Notice the left fraction is in "small arcs" and the right fraction is all lengths.

 

So the total length around the face of the clock is the circumference and 

C=2*pi*r, or for us, the C=2*pi*8 = 16 pi = total length around the face of the clock.

 

So the proportion becomes

 

  5              x

------ = -----------------

  12          16 pi

 

Multiply both sides by 16 pi and you will find "x", the arc length  you are looking for.

 

 

80 pi

-------   =    6.66667 pi = 20.9439 inches

12