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
1.31 inches
7.85 inches
8.37 inches
23.55 inches

Answer 1

7.85 inches

The area of the face of the clock is 50.24. Using the formula for the area of a circle, pi r^2, set 50.24 = pi r^2 and solve for r. r^2 = 14 and r = 4 in this application.
The minute hand has length .25 less than that of the radius of the clock face. Therefore, the minute hand has length 3.75.

On the analog clock face, the 12-hour marks are congruent arcs, each with measure 30. From 3 to 7 is 4 four of these or 120 degrees. The arc swept by the minute hand is 120/360 or 1/3 the circumference of the clock face. 1/3 of (2 pi (3.75) ) = 78.5 inches.