Solve the problem.
-Each tire of an automobile has a radius of 2 feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 105 feet per sec? Round your answer to the nearest tenth.
A) $1002.7 \mathrm { rpm }$
B) $501.3 \mathrm { rpm }$
C) $2005.4 \mathrm { rpm }$
D) $8.4 \mathrm { rpm }$

Question

Quizplus · Accepted Answer

The circumference of a tire is given by $C = 2\pi r$, where $r$ is the radius. For a radius of 2 feet, the circumference is $C = 2\pi(2) = 4\pi$ feet. To find the revolutions per minute, we first convert the speed from feet per second to feet per minute by multiplying by 60 (since there are 60 seconds in a minute), giving $105 \times 60 = 6300$ feet per minute. The number of revolutions per minute is then the total distance traveled in a minute divided by the circumference of a tire, or $6300 / (4\pi) \approx 501.3$ rpm.

Solve the Problem 1002.7rpm1002.7 \mathrm { rpm }1002.7rpm B) 501.3rpm501.3 \mathrm { rpm }501.3rpm

Solve the Problem $1002.7 \mathrm { rpm }$ B) $501.3 \mathrm { rpm }$