Inscribed 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.

HINTS GIVEN:

(1) V = pi(r^2)(h).

(2) There are similar triangles in the cone.

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- January 23rd 2007, 04:26 PMsymmetryCylinder in a Cone
Inscribed 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.

HINTS GIVEN:

(1) V = pi(r^2)(h).

(2) There are similar triangles in the cone. - January 24th 2007, 06:33 AMearboth
Hello,

I've attached a diagram (see attachment)

You have 2 similar right triangles:

- the big one with the legs H and R

- the small on with the legs (H-h) and r.

Set up the proportion:

. Solve for r:

Plug in this term into the formula of the volume of a cylinder:

EB - January 24th 2007, 01:59 PMsymmetryok
Absolutely amazing reply and great math notes for my state exam.

Thanks!