Home
Quit
Sample Answers
3. a) Hamster cage volume: 43 500 cm3; guinea pig cage
volume: 445 096 cm3
4. Since 90 45 2, the height of the prism is 2 cm.
5. Since 186.0 1.6 116.25, the base area of the prism
42 cm3
is 116.25 cm2.
6. There are 6 possible prisms with whole-number dimensions:
1 cm by 1 cm by 24 cm, 1 cm by 2 cm by 12 cm,
1 cm by 3 cm by 8 cm, 1 cm by 4 cm by 6 cm,
2 cm by 2 cm by 6 cm, 2 cm by 3 cm by 4 cm
I used the factors of 24 to find all possible prisms. I know the
prisms are different because no two prisms have the same
length, width, and height.
Some possible prisms with decimals as dimensions include:
2.5 cm by 1.6 cm by 6 cm, 1.2 cm by 2.5 cm by 8 cm,
3.75 cm by 3.2 cm by 2 cm, 1.5 cm by 2.5 cm by 6.4 cm
60 cm3
180 cm3
4000 cm3
Estimates will vary.
1944 cm3
2700 cm3
23.826 cm3
222.95 cm3
About 10 times as great
Ask:
Practice
• How can you find the volume using
mental math?
(I have to multiply 21 4 5. I multiply
4 5 first to get 20. Then I multiply 20 21
as 10 2 21. This is 10 42, or 420.)
• Would a rectangular prism with length 21 cm,
width 4 cm, and height 5 cm have the same
volume as a rectangular prism with length
4 cm, width 21 cm, and height 5 cm? Explain.
(Yes; the prisms are the same. Their orientations
are different, but they take up the same amount
of space.)
• What about a prism with length 5 cm,
width 21 cm, and height 4 cm?
(It would also be the same.)
Questions 2, 3, 5, and 7 require the use of
a calculator.
10
Unit 9 • Lesson 2 • Student page 330
Assessment Focus: Question 6
Some students will work systematically to find
all the different prisms with whole-number edge
lengths. Other students may find it helpful to
use centimetre cubes. Students should be aware
that the dimensions of a prism can be arranged
in different ways, but the prisms are congruent.
For example, a 2-cm by 3-cm by 4-cm prism
is the same as a 3-cm by 2-cm by 4-cm prism,
since both prisms have the same volume.
A Level 4 response would include dimensions
that are decimals, such as 1.5 cm by 2.5 cm by
6.4 cm. Students will need to use calculators
to determine these dimensions.
Home
Quit
7. b) The volume of the piece of cheese is 10.625 cm3, so it is
less than 1 serving.
2 cm
8. c) There are two possible arrangements when each layer
116.25 cm2
15.625 cm3
52 500 cm3; 750 cm3
70 blocks
6 ways
has a height of 5 cm; one uses 54 blocks, the other
60 blocks.
There are two possible arrangements when each layer has
a height of 10 cm; one uses 60 blocks, the other 63 blocks.
There are two possible arrangements when each layer
has a height of 15 cm; one uses 60 blocks, the other
70 blocks.
d) There is only one arrangement where all 70 blocks fit.
There are spaces left in all other arrangements, so
70 blocks do not fit.
e) The best way to pack the box is to orient the blocks so
that the 10-cm lengths fit along the 50-cm edge, the 5-cm
lengths fit along the 35-cm edge, and the 15-cm lengths
fit along the 30-cm edge. This way the blocks completely
fill the box.
REFLECT: You can divide the volume of a rectangular prism by
its height to get the area of the base of the prism. For example,
a rectangular prism with volume 10 cm3 and height 2 cm has
a base area of 5 cm2, because 10 2 5.
Numbers Every Day
Find the factors of 30 to determine the two unknown numbers.
They could be 1 and 30, 2 and 15, 3 and 10, or 5 and 6.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students understand that the amount of
space an object takes up is its volume.
✔ Students understand that the volume of
a rectangular prism can be determined
using a formula.
Extra Support: Students can do the Additional Activity,
What Will It Hold? (Master 9.8).
Students can use Step-by-Step 2 (Master 9.12) to complete
question 6.
Accuracy of procedures
✔ Students can estimate and find the
volume of rectangular prisms using
a formula.
Problem solving
✔ Students can solve problems related
to the volumes of rectangular prisms.
Extra Practice: Have students work in pairs. Students take
turns to find the dimensions of a rectangular prism with volumes
from 50 cm3 to 100 cm3. Students are permitted to have two
dimensions of 1 cm only when no other dimensions are possible.
Students can complete Extra Practice 1 (Master 9.18).
Extension: Students can do the Additional Activity,
Double Up! (Master 9.9).
Recording and Reporting
Master 9.2 Ongoing Observations:
Measurement
Unit 9 • Lesson 2 • Student page 331
11