2 Calculus II

In this class,

• Questions must be answered in order asked.
• Solutions must be neat.
• Solutions must be exact and fully simplified.
• You must use the given symbols.
• You must show all reasoning.
• Copying is never allowed, even when working together.

1. For a conical tent of given volume, find the ratio of the height $h$ to the radius of the base $r$ that requires the least amount of material. Note: prove first that the surface area of a cone (without base) is $\pi{}r\sqrt{r^2+h^2}$. ¹. [1, Maximum and Minimum Values]
2. Inside a conical tent of height $h$ and radius of the base $r$, a living space is to be partioned in the shape of a circular cylinder with a flat top of radius $R$ and height $H$. (a) Find the living space with the largest possible volume. (b) Find the living space with the largest curved surface.². [1, Maximum and Minimum Values]

¹ Include a plot and picture

² Include graphs of the functions being maximized and a picture of the tent and cylinder