Geometry Problem about Hole Placement on PVC Pipe

You need to use the arc length formula on a circle, i.e.
\[L=r \times \theta,\]
where $r$ is the radious of the circle and $\theta$ is th angle corresponding to the arc length. See: https://www.cuemath.com/geometry/arc-length/

It is important that $\theta$ should be measured in radians in the above formula. If your angles are in degrees, then the formula would be
\[(*)    L= \frac{\pi }{180}(r\theta).\]

Since the circumference of the pipe is 3 inches and 7/16 which can be written as 55/16. We have
\[55/16=C=2\pi r    \Rightarrow r=\frac{55}{32 \pi}.\]
Replacing $r$ in formula (*) we get 
\[ (**)    L= \frac{\pi }{180}(\frac{55}{32 \pi} \theta)=\frac{55}{5760} \theta.\]

Using the above fromula, lets try to answer your question now. 

- How far from your original mark should I measure to get 10 degrees?
Using the formula (**) we get 
\[L=\frac{55}{5760} \times 10=0.0955   \text{inch}.\]

- How far from your original mark should I measure to get 25 degrees?
Using the formula (**) we get
\[L=\frac{55}{5760} \times 25=0.2387   \text{inch}.\]

Leave a comment if you need any calrifications.