A silo (a structure designed to store grain) is designed as a cylinder with a cone on top, as shown in the diagram at right.  

1. If a farmer wants to paint the silo, how much surface area must be painted?

   Hint (a):

   Find the surface area of the cone, and the surface area of the cylinder.
   Then find their sum.

   Answer (a):

   The slant height of the cone $\approx9.22$ m
   Lateral Area (cone) $=6\pi(9.22)\approx173.78$
   Lateral Area (cylinder) $=12\pi(11)=132\pi\approx414.69$
   $173.78+414.69=588.47m^2$

2. What is the volume of the silo? That is, how many cubic meters of grain can the silo hold?

   Hint (b):

   Find the volume of the cone and the volume of the cylinder.
   Then find their sum.