Question

suppose the tip of the minute hand of a clock is 8 inches from the center of the clock. determine the distance traveled by the tip of the minute hand in 30 minutes. give an exact answer.

a. 4π in.
b. 16π in.
c. 64π in.
d. 8π in.

Explanation:

Step1: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C = 2\pi r\), where \(r = 8\) inches. So \(C=2\pi\times8 = 16\pi\) inches. This is the distance the tip travels in 60 minutes (a full - circle).

Step2: Find the distance in 30 minutes

Since 30 minutes is half of 60 minutes, the distance \(d\) traveled in 30 minutes is half of the circumference. So \(d=\frac{1}{2}\times16\pi=8\pi\) inches.

Answer:

D. \(8\pi\) in