Alright..

1) Find the dimension of the rectangle of the largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle.

Ok... so, for the rectangle... the height will be y... and the length is x..

Area = XY, Perimeter = 2x+2y, etc.

For the triangle, the base is B, and ive been told the height is (Radical3 over 2)times B. Why is this true? I think i forgot my triangles...

and after that, where do i go then to get to the max area.

2) A cone-shaped drinking cup is made from a circular piece of a paper of radius R by cutting out a sector and joining the angles CA and CB. Find the maximum capacity of such a cup.

and lastly, 3) A cone with height h is inscribed in a larget cone with a height H so that its vertex is at the center of the base of the larger cone. show that hte inner cone has a maximum volume when h = (1/3)H

If you can show me how to work these specific problems Itd be greatly appreciated. I have a test tomorrow and the more information I know, the better.

Thanks!