GMAT MATH : Word Problem - Geometry

Question

A point on the rim of a circular tire that is rotating in a plane is 6 inches from the center of the rim. What is the distance traveled, in inches, by this point in 10 seconds when the tire turns at the rate of 250 revolutions per minute?

A) 36000π
B) 6000π
C) 3000π
D) 500π
E) 1000π 

 Solution

 Answer D

Area covered by a circle is equal to its circumference, which is calculated by 2πR 
If a point is 6 inches from the center of the rim and it rotates in a circle, then radius (R) of the circle is 6 inches.
So the distance covered by one rotation of the rim is  2 (π) (6) = 12π
Distance cover in one minute; based on the information provided in the Question the rim makes 250 revolutions per minute.
Distance covered in 250 revolutions = 12 (π) (250).
The Question wants us to know how far the rim travels in 10 seconds. This can be calculated by multiplying the total distance traveled by (10/60) (10 seconds of 60 seconds of minute).
   12 (π) (250) (10/60) = 500π