Answer:
1.83 inches
Step-by-step explanation:
Given:
Length of minute hand = 6 inches
To find: Distance traveled by the minute hand between 10:25 a.m and 11:00 a.m
Solution:
Let [tex]l[/tex] denotes arc length, [tex]r[/tex] denotes radius and [tex]\theta[/tex] denotes central angle subtended by the arc
So, [tex]l=r\theta[/tex]
Angle subtended by an arc in 1 minute [tex]=\frac{1}{2}^{\circ}[/tex]
So, angle subtended by an arc in 35 minutes [tex]=\frac{35}{2}^{\circ}=17.5^{\circ}[/tex]
[tex]=17.5\times \frac{\pi}{180}\\=\frac{17.5\pi}{180}[/tex]
Here, [tex]r[/tex] = Length of minute hand = 6 inches
So,
[tex]l=6\left ( \frac{17.5\pi}{180} \right )=\frac{6\times 17.5\times 22}{7\times 180}=1.83[/tex] inches
