The Clean-Up Vacuum Company is designing a new upright vacuum cleaner.

1. What shapes can they use to model this new vacuum cleaner?

   Hint (a):

   Which 3-dimensional shapes can stand on their own?

   Help (a):

   Think of how each piece will be used.

2. The Clean-Up Vacuum Company has decided to use a cylindrical model for the body of the vacuum. They want it to be $2.5$ feet tall and have a circumference of $14$ inches. If only $75\%$ of the cylindrical body can hold the dirt from cleaning, how much dirt can the new upright vacuum hold?

   Hint (b):

   Use a diagram to visualize the dimensions of the cylinder.

   Help (b):

   Recall the equation for the circumference.
   How can that help you determine the radius of the cylinder?

   More Help (b):

   $75\%$ of the body refers to $75\%$ of the volume.

   Answer (b):

   $≈ 350.94$ cubic inches