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#1 2024-04-27 08:23:42
- mathxyz
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- From: Brooklyn, NY
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Cylinder In A Cone
Inscribe a right circular cylinder of height h and radius r in a cone of fixed radius R and fixed height H. Express the volume V of the cylinder as a function of r.
Let me see.
I am thinking volume of a cylinder formula: V = pi•r^2 h.
For some reason, similar triangles may apply here but I am guessing, of course.
I need guidance here....
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#2 2024-04-27 20:02:50
- Bob
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Re: Cylinder In A Cone
It's that word inscribed again. If you sketch the cone as an isosceles triangle with height H and base radius R, the cylinder fits inside so that its base rests on the base of the cone with common centre of the two circles (R and r) and the top of the cylinder also touches the side of the cone h units above the base.
Your sketch should will then show the similar triangles, cone H high and base R, cylinder h high and base r.
Because they are similar h/r = H/R. That's needed because you can express h in terms of the other variables and hence eliminate h from the volume equation leaving r, R and H.
Bob
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#3 2024-04-28 01:26:48
- mathxyz
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- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 887
Re: Cylinder In A Cone
It's that word inscribed again. If you sketch the cone as an isosceles triangle with height H and base radius R, the cylinder fits inside so that its base rests on the base of the cone with common centre of the two circles (R and r) and the top of the cylinder also touches the side of the cone h units above the base.
Your sketch should will then show the similar triangles, cone H high and base R, cylinder h high and base r.
Because they are similar h/r = H/R. That's needed because you can express h in terms of the other variables and hence eliminate h from the volume equation leaving r, R and H.
Bob
Ok. I will try again amd only return here should I need further assistance.
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Online
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