Question

a water wheel has a radius of 12 feet. the wheel is rotating at 20 revolutions per minute. find the linear speed, in feet per minute, of the water.
the linear speed is approximately
(round to the nearest whole number as needed.)

Explanation:

Step1: Find the circumference of the wheel

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 12$ feet, so $C=2\pi\times12 = 24\pi$ feet.

Step2: Calculate the linear speed

The wheel makes 20 revolutions per minute. In one revolution, a point on the wheel travels a distance equal to the circumference. So the linear speed $v$ is the number of revolutions per minute times the circumference. $v = 20\times C=20\times24\pi$.
$v = 480\pi\approx480\times 3.14159 = 1507.9632$ feet per minute.
Rounding to the nearest whole - number, $v\approx1508$ feet per minute.

Answer:

1508