Arc of a cylinder - would appreciate help

[m32dave]

Would really appreciate help with the following:
Firstly, could someone answer this (simple?) question for something I am trying to make?
Secondly, could you give me the most straightforward formula for working it out if I change the length?

Hope this makes sense.
I have a cylinder. I have an arc exactly 2.000m long extending up from the base of the cylinder at 45 degrees following the elliptical arc. The diameter of the base is 4.990m What is the height of the arc? What is the length of the segment across the base, or the length of the arc around the cylinder base perpendicular to the end of the arc.

Big Thanks

 

[Petr Mugver]

If you "unroll" a cylinder you get a plane, so you can just use Pitagora's theorem:

height = base length = L/sqrt(2)

 

[m32dave]

If you "unroll" a cylinder you get a plane, so you can just use Pitagora's theorem:

height = base length = L/sqrt(2)

Thanks,for putting it succinctly. I figured the same thing out in my bed last night.

 

[HallsofIvy]

In bed- that's where I do my best work!

 

[CellCoree]

Hello,

The height of the arc on your cylinder can be calculated using the following formula:

h = r - √(r² - (d/2)²)

Where:
h = height of the arc
r = radius of the cylinder (d/2)
d = diameter of the cylinder

To find the length of the segment across the base, or the length of the arc around the cylinder base perpendicular to the end of the arc, you can use the formula for arc length:

s = rθ

Where:
s = arc length
r = radius of the cylinder
θ = angle in radians (in this case, 45 degrees converted to radians is approximately 0.7854)

So, the length of the segment across the base would be:
s = (4.990/2)(0.7854) = 1.9636m

I hope this helps. Good luck with your project!