Unit 7: Filling and Wrapping
Investigation 1.1 - How Big Are Those Boxes?
Name
ey
A. Label each measurement below on the diagram.
1. Length V
2. Width V
3. Height V
4. Diagonals
Explain how each measurement below relates to the diagram above.
5. Surface Area-
6. Volume-
The amouni- Of hia+erial needed 1-o coy)struck
+he walls (faces) of The box.
The amouni- 0C space inside the box.
B. Match each of the possible measurements in the word bank below to the questions they would help to
answer. You may use more than one measurement for each question.
1. How much paint would you use to paint the container in a new color?
Word Bank
Length
Surface area
2. Could you store a small car in the container?
Width
length, Width ) heigh+
Height
3. How many sacks of rice, corn, or black beans could you store in
the container?
Diagonals
Surface Area
volume
4. Could you store pipes for a farm sprinkler system in the container?
Volume
length and/or diagonals
5. Could you store a long flag pole in the container?
ter)0+11 and/Or di a30)160
Filling and Wrapping
S
Investigation 1 Building Smart Boxes: Rectangular Prisms
C. The filled shipping containers are stacked on a ship. The load is built up in layers.
Load 3
Load 2
Load 1
1. How could you calculate the number of containers in 1 layer of a load?
lens+h X wid+h
2. How could you then calculate the total number of containers in each load?
Load 2
Load 3
Load 1
.
5 XLi — [20
T
1.
Imp vvid-th
5xl-ix2.= 1-10
base
/r
5x4x
base
i# layers
5=
14 L.
1(4
-th'aye rs
3. Suppose a ship's load has 10 containers in each row from one side to the other, 15 containers in
each row from front to back, and 8 layers of containers. How many containers are in the whole
load? (Use blocks or a sketch to help you)
15 10 X
base
Filling and Wrapping
= L I2001
,
lcmcrs
Investigation 1 Building Smart Boxes: Rectangular Prisms
D. Basketballs are spheres, but they are often packaged in boxes in the shape of cubes.
1. How many of these boxes would fit into a shipping container that is 6 feet long by 5 feet wide
by 4 feet high? (Use blocks or a sketch to help you) Describe the arrangement
- ''es.
X 5 X =
D20 f-1- 3
120 of The- baske+loalt
boxes would fif inside
+he container.
5f+
(of+
2. What are the dimensions of some other rectangular containers that would hold the same
number of basketball boxes? Describe the arrangement of the boxes in each case. Which
containers make the most sense? The least sense? (Use blocks or a sketch to help you)
'Theoretically) there are an inPini+c number of'
containers that wouid hold 12.0 of the baske+bail
boxes. However, -those that would hold 120
boxes 4-he isms+ ariciently, meaning with 1-he
least amount oF wasfeci space, wouici be those
with integer side len3th5 ci,i2j _c_ Such tha+
1/20. For example) an Sf+ by 5ff by 3f+
contain er would neat1y hold all 12.0 boxes.
Other examples) such as 1 20f+ by Ifi- by Iff
container) Would no+ maKe much sense since
+hey would rev ire an uneceSsarily larp amount
o-F material to construe+ the, WQIIS.
Filling and Wrapping
Investigation 1 Building Smart Boxes: Rectangular Prisms
E.
1 Layer
2 Layers
5 Layers
Prism 1
Prism 2
Prism 3
1. Find the surface area and volume of each prism in Ouestion C.
Prism 1
Prism 2
2 (1-1i-5 + 26)
Surface Area
Volume
429)
5X 1-hc I
2Dx I
- 20'
,,_.
••
Prism 3
2(8+- 10+20 2(20+25+20)
2(65)
2(38)
130.
5 xl-i x2.
20)(2
,
5xYx5
20x5
40
IOD
.
2. Describe a strategy for finding volume and surface area of a rectangular prism.
Surface area : Find the area a all six
-faces and +hen add ihem
together,
volume, Find The area oF The base
and then multiply by *ha
hei3 ht.
Filling and Wrapping
Investigation 1 Building Smart Boxes: Rectangular Prisms