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.

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

can you find the circumference of the circle the minute hand makes as it goes around?

Answer 2

then multiply that by 1/60 for every minute it sweeps in your arc

Answer 3

I got the circumference of 25.12, would that be correct?

Answer 4

you can also use s = r * theta, where s is the length of the arc, r is your radius, theta is the angle created between 3 and 7 on the clock. theta MUST be in radians.

Answer 5

I'm still not entirely sure how to solve this problem or where to start

Answer 6

well, you know the surface are of the clock... so what is the radius?
can you do that?

Answer 7

would the radius be 4?

Answer 8

yes

Answer 9

now subtract the gap for the minute hand to get the radius of the smaller circle

Answer 10

then get that circumference

Answer 11

i got 11.775 for the circumference

Answer 12

what is the formula for circumference and what is the radius you used?

Answer 13

not saying you are wrong, but that is half of what I thought it was

Answer 14

I used the radius 3.75 and but i forgot to multiply by 2, oops. I got the answer of 23.55 just now. I used the forumla 2 * 3.14 * 3.75

Answer 15

ok, thats what I thought it was... maybe we are both right (crossing fingers)

Answer 16

so every minute sweeps out 1/60 of that 23.55 inches...

Answer 17

and you want to know how far it swept in 4 minutes...

Answer 18

so would i multiply 1/4?

Answer 19

no that would be 15 minutes (dont get confused)

how many inches does it go in one minute?
remember it goes 23.55 inches in 60 minutes

Answer 20

2.54? I got that by dividing 23.55 into 60

Answer 21

ok, step back and think about that... does the minute hand move 2.54 inches every minute? when it moves 23.55 inches in an hour?

Answer 22

I think you did it backwards... should be a very small answer

Answer 23

so what would i do to figure out how far it moves

Answer 24

23.55/60 should tell you how many inches that sucker moves every minute

Answer 25

so how far does it go in 4 minutes?

Answer 26

0.3925

Answer 27

and in 4 minutes?

Answer 28

1.57 in four minutes

Answer 29

1.57 what? and yes, I think that is the answer to this puzzle

Answer 30

well the answer options i was given for this question were
1.31 inches
7.85 inches
8.37 inches
23.55 inches
so i'm not sure if it could be that many inches

Answer 31

so where did we/I mess up? hmmm

Answer 32

circumference is 2 pi r ?

Answer 33

yes

Answer 34

ok I got it
it is not 4 minutes... it is the minutes between the 3 and the 7 on the clock
how far did that sucker go in 20 minutes?

Answer 35

7.85!

Answer 36

so we didnt mess up after all, well, not much...
have a great day

Answer 37

thanks :)