Geometry
Chapter 9, Surface Area and Volume
Once packages are designed, they may be painted or labelled for decoration or identification. It is necessary to find the areas of the sides and faces of these containers first.
Part A, Surface Area of Prisms
1. Go to the Jos Steeman
Alkmaar BV Web site to see dimensions for three different sized
cargo containers. Each of these containers has six sides made of steel.
Find the surface area of the 20 Foot Dry Cargo Container in order to estimate
the amount of steel necessary to manufacture this container. Use square
feet for the surface area.
Part C, Surface Area of Cylinders and Cones
2. It is important to be able to calculate the surface area of containers in order to manufacture labels for these containers. Go to the Duvivier Web site to see an advertisement for a can labeller. You will use the technical data for Model D210 in this exercise.
a. Use the technical data at the bottom of this web site to find the minimum circumference of a container which labeller model D210 can create a label for.
b. Why is the minimum length of the label actually longer than this?
c. Find the minimum lateral surface area of a container which labeller model D210 can create a label for.
d. What is the minimum area of a label model D210 can create?
e. Why is the minimum area of the label actually less than the minimum lateral surface area of the can?
f. Why is the maximum container height 8 mm more than the maximum label width?
3. Some containers are made of a combination of three-dimensional shapes.
Go to Conical
bottom Web site to see dimensions of tanks which are shaped like
a cylinder placed on top of a cone. Look at the dimensions for model CBO-45.
Suppose that the cone and the cylinder each have a height of 21". Find
the lateral surface area of this container (excluding the top).