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?

10.68 inches

3.56 inches

6.80 inches

21.35 inches

Answer 1

6.80 inches

Answer 2

if correct please click best response

Answer 3

Could you help me with another question as well?

Answer 4

@Nurali

Answer 5

yes i will try.

Answer 6

The length of an arc is given by the formula:
\[L = \left( n / 360 \right) \times 2 \pi r\]
where L = length, n is the number of degrees of the arc, and r is the radius of the circle.
Also, the formula for the area of a circle is
\[A = \pi r ^{2}\]
Using the formula for the area of a circle, solve it for radius,
\[r = \sqrt{ A / \pi} \]
Now calculate the radius of the face of the clock:
r = sqrt(153.86/pi) = 7 in.
The length of the minutes hand is 0.2 in. less than the raduis of the face, or 6.8 in.
Now use the formula for length of arc with a raduis of 6.8 in. What number of degrees do you need to use? From 8 to 2 on a clock, it's 180 degrees.
L = (180/360) x 2 x pi x 6.8 = 21.36 in., so it looks like 21.35 incehs is the answer