1.
There are six ways to form a rectangular solid from 24 cubes (two
rectangular solids are considered the same they are congruent- if
you can flip or rotate one to match it up to another, they are the
same). Use the cubes to build the six rectangular solids. Then draw
them on the isometric paper below. Record the dimensions for your
rectangular solids so you can refer to them on the next section.
(Volume of the cube = 1 unit 3 )
2.
Count and record the dimensions of the rectangular solids.
Determine the surface area and volume for each solid you created,
recording the information on the chart below.
3.
The efficiency of a container is based on the ratio of the surface area
to volume (surface area divided by the volume). The container with
the smallest ratio uses the least surface area to cover a given volume.
A sphere is the most efficient solid. A cube is the most efficient
rectangular solid. Calculate the efficiency ratio for each solid you
created- rounding to the thousandths place. Record this amount in
the last column of the chart below.
DIMENSIONS
Length · width · height
4.
SURFACE
AREA
(SA)
VOLUME
V
EFFICIENCY
RATIO:
(SA / V)
Write a clear explanation answering the following questions:
a. How is the shape of a solid related to its surface area?
b. How can you tell which solid makes the most use of the square
units that cover it?
c. What does the ratio of the surface area to volume tell you about
the shape?