OpenStudy (anonymous):

A cylinder is inscribed in a right circular cone of height 3.5 and radius (at the base) equal to 2.5. What are the dimensions of such a cylinder which has maximum volume?

6 years ago
OpenStudy (anonymous):

So if you draw the diagram and look at it from the side, it looks like a triangle with height 3.5 and base 2.5*2 = 5. Therefore for any height h from the top, we will have a base b with the same proportion. That is, h / 3.5 = b / 5. But now we see that b is in fact the diameter of the cone, and (3.5-h) is in fact the height of the cone! So volume of cone = height*pi*r^2 = (3.5-h)*pi*(b/2)^2 = (3.5-h)*pi*b^2/4 = (3.5-h)*pi*(5h/3.5)^2/4 . Now that we have the volume of the cone in terms of one variable, we take the derivative and set it equal to 0, allowing us to find a local maxima.

6 years ago