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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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....

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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.