I was thinking of a question for a while now. enter image description here

R1 is radius of small circle, R2 is radius of large. The small circle is actually the base of a right cylinder and the big circle is the top. So in reality R1=R2. Given that R2=k*R1, k is some proportion, in the picture is there a way to determine the height of the cylinder?

I came to this question because originally I was thinking if there is a way to figure out the distance from observer A to B with a camera. You essentially move the camera upwards perpendicular to ground by x meter at the same time detecting by how much observer B moved (just like the cylinder question distance B moved is simply how it looks like on 2D).

Thanks ahead of time.


If $V$ is the viewpoint, then it must be aligned with the cylinder axis (dashed line in the diagram below), which in turn is perpendicular to the view plane $\pi$. If $v$ is the distance between $V$ and $\pi$ and $d$ is the distance between $\pi$ and the front base of the cylinder, then by similar triangles we have:

$$ R_2:R=v:(v+d), \quad\hbox{and}\quad R_1:R=v:(v+d+h). $$ By dividing the first equation by the second we obtain: $$ R_1:R_2=(v+d+h):(v+d). $$ To solve for $h$ you then need to know $d+v$.

enter image description here


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.