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

k

Answer 2

tips?

Answer 3

find the radius of the clock from its area
find the radius of the min hand
find the angle of the arc traveled between 3 and 7
arc length = r * theta (in radians)

Answer 4

k....

Answer 5

the radius is 4....

Answer 6

and the radius of the min hand is 3.75

Answer 7

Am I going in the right direction?

Answer 8

yes

Answer 9

k

Answer 10

I think that the angle of the arc traveled is 120 degrees

Answer 11

so 3.75 the radians?

Answer 12

can you give me a hint?

Answer 13

one way to think of it: all the way round is the circumference of a circle with radius 3.75
you want 1/3 of that

Answer 14

approximately 7.85!!!!

Answer 15

yes

if you use radians instead of degrees, then the angle is 2 pi/3 radians
and
\[ s= \frac{2 \pi}{3} r \]
which as you can see is the same as 1/3 of all the way around = \( 2 \pi r\)

Answer 16

yeah!!!!!!!!!!!!!!!!!!!!!

Answer 17

one more please?

Answer 18

\[ 120º * \frac{ \pi}{180} = \frac{2}{3} \pi \text{ radians}\]

Answer 19

k