Answer:
18.8 inches
Explanation:
You want the length of arc traveled by the tip of a 4" minute hand moving from 1:30 pm to 2:15 pm.
Arc
The time difference between 2:15 and 1:30 is 45 minutes, or 3/4 hour. The minute hand moves through an angle of 2π radians in 1 hour, so will move through an angle of (3/4)(2π) = 3/2π radians in 3/4 hour.
Length
The length of an arc is given by the formula ...
s = rθ
where r is the radius, and θ is the central angle in radians.
Here, we have r = 4 in, and θ = 3π/2. The arc length is ...
s = (4 in)(3π/2) = 6π in ≈ 18.8496 in
The minute hand moves through an arc of about 18.8 inches from 1:30 to 2:15.