Posted by Jake Monroe on .
Karen makes pottery on a pottery wheel. Today she is making vases that are in the shape of a circular cylinder that is open at the top, that is, it has only one base. The base has a radius of 4.5 centimeters and 0.75 centimeters thick. The lateral surface of the cylinder will be 0.4 centimeters thick. She uses 206 cubic centimeters of clay for each vase.
a. How much clay is used for the base of the vase to the nearest tenth.
b. How much clay will be used for the lateral surface of the vase to the nearest tenth
c. How tall will the vase be to the nearest tenth?
c. What will be the lateral surface to the nearest tenth. ( Use the value of the height of the vase found in part c.

Geometry 
Steve,
The volume of clay is for a cylinder of radius r is
pi r^2(0.75) + pi(r^2(r.4)^2)h = 206
Since we have r=4.5, h = 14.6 cm
The base is easy, and just subtract that from 206 to get the lateral volume.
The lateral surface is just 2pi r h