Cylinders and Cones

[legacyofpiracy]

I am still struggling with these sort of problems and I was wondering if anyone could sort of nudge me along?

Here is the problem:

A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 4. What are the dimensions of such a cylinder which has maximum volume?

Well starting with the basics I know the volume of the cone to be 41.8879 (just plugging in the given into the volume equation) but now I am confused as to where to attack next.

Any help would be greatly appreciated

 

[Lizzie]

haha, you sound JUST LIKE ME! I don't know how to help you though, I'm sorry.

 

[legacyofpiracy]

thanks anyway

 

[stapel]

Draw the cross-sectional view, so you have an isosceles triangle with a rectangle inside it. The rectangle is centered on the height line of the triangle, with its base on the base of the triangle and its upper corners touching the sides of the triangle.

Label half of the rectangle base as "x" and its height as "y". Then use similar triangles to figure out a relationship between x, y, h = 2.5, and r = 4. Then work with the volume formula for a cylinder to come up with the function you need to maximize.

Eliz.