Solve the problem.
-Suppose the tip of the minute hand of a clock is 8 in. from the center of the clock. Determine the distance traveled by the tip of the minute hand in $3 \frac { 1 } { 2 }$ hours. Give an exact answer.
A) $24 \pi \mathrm { in }$.
B) $56 \pi \mathrm { in }$.
C) $32 \pi \mathrm { in }$.
D) $48 \pi \mathrm { in }$.

Question

Quizplus · Accepted Answer

The distance traveled by the tip of the minute hand in one complete revolution is the circumference of the circle it traces, which is given by $C = 2\pi r$, where $r$ is the radius of the circle. Here, $r = 8$ inches, so $C = 2\pi(8) = 16\pi$ inches per revolution. In $3 \frac{1}{2}$ hours, or $3.5$ hours, the minute hand completes $3.5 \times 60 = 210$ minutes of travel, equivalent to $210 / 60 = 3.5$ complete revolutions. Therefore, the total distance traveled is $3.5 \times 16\pi = 56\pi$ inches.

Solve the Problem 3123 \frac { 1 } { 2 }321​

Solve the Problem $3 \frac { 1 } { 2 }$