|
a. |
What
are the length, width, and height of the prism? |
|
b. |
How
much material would be needed to make a box for the prism? |
|
c. |
How
many blocks are in the prism?
|
| 4. |
Suppose
you want to make a box to hold exactly thirty 1-inch cubes. |
|
a. |
Describe
all the possible boxes you could make. |
|
b. |
Which
box has the least surface area? Which has the greatest surface
area? |
|
c. |
Why
might you want to know the dimensions of the box with the
least surface area?
|
| 5. |
a. |
Sketch
a rectangular box with dimensions 2cm by 3 cm by 6 cm. |
|
b. |
What
is the surface area of your box? |
|
c. |
Sketch
a flat pattern for your box. What is the relationship between
the area of the flat pattern and the surface area of the box?
|
|
Answers
Applications
(Note: To find the number of blocks in questions 1-3, some students
may count cubes; others may multiply measures. To find the surface
area, some students may try to count the faces of the cubes shown;
some may add the areas of the faces. What is important at this
stage is that they understand that the amount of wrapping is called
the surface area.)
| 1a. |
l =5
in, w =3 in, h =1 in |
| 1b. |
46
sq. in. |
| 1c. |
15
blocks |
| 2a. |
l =5
in, w =3 in, h =2 in |
| 2b. |
62 sq. in. |
| 2c. |
30
blocks |
| 3a. |
l =5
in, w =3 in, h =5 in |
| 3b. |
110
sq. in. |
| 3c. |
75
blocks |
| 4a. |
There
are five possible boxes: 1 by 1 by 30, 1 by 2 by 15, 1 by
3 by 10, 1 by 5 by 6, and 2 by 3 by 5. |
| 4b. |
The
2 by 3 by 5 box has the least surface area, 62 sq. in. The
1 by 1 by 30 box has the greatest surface area, 122 sq. in. |
| 4c. |
Possible
answer: It will cost less to make the box with the least surface
area. Also, it might be easier to pack these boxes into a
larger box. |
| 5a. |
Possible
sketch:  |
| 5b. |
72
sq. cm. |
| 5c. |
Possible
flat pattern:  |
| |
The
area of the flat pattern is the same as the surface area of
the box. |
|
