Posted by **Anamika** on Thursday, December 20, 2012 at 12:29pm.

Prove that the radius of the base of right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half that of the cone

- maths --plse help me.. -
**Steve**, Thursday, December 20, 2012 at 2:48pm
Hmm. If the cone has radius R and height H, and the cylinder has radius r and height h,

by similar triangles, r/R = (H-h)/H

area of cylinder

a = 2pi r h

= 2pi (R/H) h(H-h)

da/dh = 2pi (R/H) (H-2h)

max a when H = 2h

or, if you don't have calculus to help you, let's pick up here:

a = 2pi (R/H) h(H-h)

= 2pi (R/H) (Hh - h^2)

this is a parabola with vertex (maximum value) when h = H/2

## Answer this Question

## Related Questions

- Calculus - A right circular cylinder is inscribed in a cone with height h and ...
- maths - Two spheres of radius 6 cm and 4cm are inscribed in a right circular ...
- Maths - Find The altitude of a right circular cone of maximum curved surface ...
- maths-surface area - A solid is in the form of cone mounted on a hemisphere in ...
- math - A right circular cylinder of radius r and height h is inscribed in a ...
- Calculus - Given a right circular cone, you put an upside-down cone inside it so...
- math - Find the altitude of a right circular cone of maximum curved surface ...
- Math - An inverted right cone, half filled with water. I've only the volume of ...
- Calculus: Optimization - I have no idea how to approach this problem, if someone...
- Math - Calculus I - Optimization Problem: Find the dimensions of the right ...