Answer:
[tex]16.2\ \frac{rev}{min}[/tex]
Step-by-step explanation:
The complete question is
A hamster runs at 17 centimeters per second in a wheel of radius 10 centimeters how fast will the wheel spin in revolutions per minute?
step 1
Find the circumference of the wheel
The circumference of the circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=10\ cm[/tex]
substitute
[tex]C=2\pi (10)\\C=20\pi\ cm[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]C=20(3.14)=62.8\ cm[/tex]
step 2
Find the number of revolutions
Remember that
One revolution of the wheel represent a distance equal to the circumference of the wheel
using proportion
[tex]\frac{1}{62.8}\ \frac{rev}{cm}=\frac{x}{17}\ \frac{rev}{cm}\\\\x=17/62.8\\\\x=0.27\ rev[/tex]
so
The number of revolutions per second is [tex]0.27\ \frac{rev}{sec}[/tex]
step 3
Convert to rev per minute
we know that
[tex]1\ min=60\ sec[/tex]
to convert sec to min divide by 60
so
[tex]0.27\ \frac{rev}{sec}=0.27:\frac{1}{60}=16.2\ \frac{rev}{min}[/tex]
