Measurement – AP Book 7, Part 2: Unit 2
AP Book ME7-22
2.
a)
Right prisms: A, B, F
page 42
Skew prisms: D, G
1.
Not prisms: C, E
a)
4  5 = 20
4  4 = 16
b)
20
16
c)
3
3
d)
20  3 = 60
16  3 = 48
2.
4.
E: opposite bases
aren’t connected by
parallel lines.
C: bases are not
congruent polygons.
lw
3.
Teacher to check.
b)
h
4.
Teacher to check drawing.
c)
lwh
Good skeletons: a), d)
volume = length 
width  height
In b), edges of bases
overlap.
a)
d)
3.
b)
c)
4.
1 1
2;2
5.
1
2
6.
a)
1
2 ; 16; 8
b)
1
2 ; 54; 27
c)
1
2 ; 27; 13.5
d)
1
2 ; 160; 80
e)
1
2 ; 36; 18
f)
1
2 ; 450; 225
In c), a pair of corners are
in alignment so 2 edges
overlap.
5.
Teacher to check.
a)
width: 2 blocks
6.
Teacher to check.
AP Book ME7-25
length: 2 blocks
7.
a)
page 48
B: 2 km, 4 km, 4 km
ii)
12 cm
3
iii)
8 cm
iv)
12 cm
i)
6 cm
ii)
12 cm
AP Book ME7-24
iii)
8 cm
page 46
iv)
12 cm
Volume B: 32 km
height: 2 m
Volume C: 105 m
3
8.
width: 2 cm
Answers will vary –
teacher to check.
A.
B.
length: 4 cm
height: 2 cm
Volume = 16 cm
3
2
D.
i)
1 cm
ii)
2 cm
a)
1
2
iii)
2 cm
AP Book ME7-23
b)
2
iv)
3 cm
page 43
c)
i)
i)
6 cm
ii)
24 cm
3
iii)
16 cm
3
36 cm
3
1.
2.
Teacher to check shading
of bases is correct.
a)
i)
ii)
iii)
b)
c)
ii)
V of r.p. = 70
V of t.p. = 35
iii)
Pentagonal
prism
V of r.p. = 40
V of t.p. = 20
3.
a)
Rectangles
b)
i)
1
ii)
5
iii)
4
i)
14=4
i)
6
ii)
5
ii)
5  7 = 35
3
iii)
4  5 = 20
iii)
AnswerKeysforAPBook7.2
E.
V of t.p. = 4
Hexagonal
prism
Triangular
prism
V of r.p. = 8
24 cm
3
ii)
55 cm
3
iii)
21 cm
3
E.
Yes.
1.
Conjecture:
Volume of a right prism =
(area of base) × height
a)
2.
a)
Area of base =
(3 × 4) + [(2 × 3) ÷ 2]
= 12 + 3 = 15;
Volume = 15  2
3
= 30 cm
b)
Area of base
= (6 × 4) = 24;
Volume = 24  3
3
= 72 cm
Area of base =
(4 × 6) + [2 × (6 × 2)
÷ 2] = 24 + 12 = 36;
Volume = 36  5
3
= 180 cm
3
By the number of layers
G.
Volume of a rectangular
prism = (area of the base)
 height
3.
i)
12 cm
2
ii)
11 cm
2
iii)
7 cm
a)
Triangle
b)
The volume of a
triangular prism
=lwh÷2
= (l  w  2)  h
= (area of triangular
base)  height
4.
INVESTIGATION 2
2
Area of base =
(4 × 2) ÷ 2 = 4;
Volume = area of
base  height
3
= 4  3 = 12 cm
c)
F.
A.
Area of base =
(3 × 2) ÷ 2 = 3;
Volume = area of
base  height
3
= 3  3 = 9 cm
The numbers are all the
same, only the units differ.
iv)
3
Yes, they are all made up
of two congruent polygons
(the bases) connected by
parallel lines.
3
4
3
i)
3
2
Volume = 30 m
7 cm
3
c)
height: 5 m
iii)
3
b)
length: 3 m
a)
3
2
C.
1.
width: 2 m
11 cm
2
1
2
d)
ii)
2
3
length: 3 m
3
b)
6 cm
3
b)
12 cm
INVESTIGATION 1
i)
Volume A: 36 cm
width: 2 m
Volume = 12 m
c)
3
i)
D.
A: 3 cm, 3 cm, 4 cm
Volume = 8 blocks
b)
C: 5m, 3m, 7m
B.
C.
In a volume calculation,
the length occurs – and
is multiplied together –
three times.
height: 2 blocks
COPYRIGHT©2010JUMPMATH:NOTTOBECOPIED
The numbers are
the same.
a)
Volume of t.p.
= 15  h
Volume of r.p.
= 20  h
Volume of full prism
= 15  h + 20  h
U‐11
b)
c)
Yes (distributive law)
5.
a)
The area of the
base is (15 + 20),
so the volume of:
15  h + 20  h
Left: 8 cm
b)
336 cm
c)
1 125.3 cm
Back: 15 cm
Left: 12 m
Teacher to check.
7.
a)
1 000 mL
b)
1 000 cm
a)
V = 1 000 cm
d)
3
3
6.
a)
V = 10 000 cm
c)
V=1m
i)
ii)
3
C=1L
425 mL
b)
336 mL
c)
1 125.3 mL
1 890 cm
11.
20 cm since:
b)
2
Volume = (Area of base)
 h so (Area of base) =
Volume  h or 300  15
12.
80 cm
BONUS
f+b=92
2
= 18 cm
7.
a)
2
b)
h = (250 ÷ 49) + 4.5
Teacher to check.
a)
1 cm
b)
3 cm
c)
5 cm
a)
Teacher to check.
b)
Front: 3 cm
7.
66 cm
b)
Triangular prism
c)
Rectangular prism
c)
Triangular prism
Square prism
b)
Teacher to check.
9.
a)
b = 2  3 = 6 cm
t = 3  1 = 3 cm
Rectangular prism
Back: 3 cm
2
2
Left side: 2 cm
add everything in b)
2
together: 22 cm
Teacher to check.
U‐12 2
t = 2  4 = 8 cm
Teacher to check shading
of bases is correct.
# sides on base
3
4
5
6
# rectangular
faces (non-base)
3
4
5
6
4.
2
# of sides on the base =
# of non-base rectangular faces
5.
2
2
2
2
surface area
2
= 28 cm
10.
Teacher to check nets.
a)
surface area: 42 cm
volume: 18 cm
3
2
c)
24 m
3
2
a)
94 cm
b)
40 cm
c)
52 cm
2
2
She can multiply 20 by 2
since the s.a. of the back,
bottom, and left faces is
equal to the s.a. of the
front, top and right faces.
Only 3 of the 6 are correct:
(area of top + area of left
side + area of back)  2
2
b = 2  4 = 8 cm
Teacher to check.
60 m
(area of bottom + area of
left side + area of front)  2,
2
2
lf = 1  2 = 2 cm
a)
b)
(area of top + area of right
side + area of front)  2
2
b = 1  4 = 4 cm
2
2.
1.
2
rf = 1  2 = 2 cm
Bottom: 6 cm
4.
f = 1  4 = 4 cm
2
2
page 56
2
b = 3  1 = 3 cm
2
AP Book ME7-28
3.
d)
Top: 6 cm
Right side: 2 cm
12.
Square prism
surface area =
2
22 cm
2
lf = 1  4 = 4 cm
38 cm
2
2
rf = 1  4 = 4 cm
2.
b)
b)
2
2
b = 1  3 = 3 cm
Smallest rectangle
is missing; teacher
to check drawing.
lf = 2  1 = 2 cm
Square prism
Teacher to check.
t = 4  3 = 12 cm
f = 1  3 = 3 cm
Smaller rectangle is
missing; teacher to
check drawing.
rf = 2  1 = 2 cm
a)
a)
c)
2
3
b)
In a): Net 3 has
both bases on the
same side.
8.
2
288 cm
surface area: 62 cm
b = 4  3 = 12 cm
Teacher to check nets.
2
c)
11.
2
3
volume: 30 cm
Teacher to check.
a)
Yes, since two
of the dimensions
(length and width)
are the same.
page 53
1.
2
ii)
page 51
3.
a)
b)
6.
62 cm
AP Book ME7-27
2.
5.
2
i)
c)
In b): Net 1 has a
base that isn’t an
equilateral triangle
but all rectangular
sides are equal;
Net 3 has bases
oriented in opposite
directions.
t + b = 15  2
2
= 30 cm
AP Book ME7-26
1.
c)
r + l = 12  2
2
= 24 cm
3
10.
Net 2 only
2
t + b = 12  2
2
= 24 cm
a)
b)
r + l = 10  2
2
= 20 cm
3
C = 10 000 mL
9.
2
Nets 1 and 2
surface area: 28 cm
volume: 8 cm
2
a)
No, he’s only
counted half the
faces; it is actually
2
52 cm .
C = 1 000 mL
b)
4.
2
Bottom: 18 m
3
b)
1
2
Left: 10 cm
Back: 6 m
6
1
Bottom: 6 cm
3
6.
8.
b)
2
2
c)
b)
a)
2
2
3
425 cm
3.
Bottom: 12 cm
= (Area of base)  h
a)
2
2
= (15 + 20)  h
5.
Back: 6 cm
(continued)
2
a)
4m
b)
3m
c)
7m
a)
5m
b)
5m
c)
4m
6.
a = 6 m, b = 3 m, c = 2 m
7.
1) Calculate the area of
each face and add
them all together.
2) Calculate the area of
the front, bottom, and
right side, add these
numbers together and
multiply by 2.
Preference will vary.
AnswerKeysforAPBook7.2
COPYRIGHT©2010JUMPMATH:NOTTOBECOPIED
Measurement – AP Book 7, Part 2: Unit 2
Measurement – AP Book 7, Part 2: Unit 2
8.
[(l  w) + (l  h) + (w  h)]
2
9.
a)
(continued)
Teacher to check.
b)
Teacher to check.
c)
bottom = 750 cm
2
2
top = 750 cm
2
front = 600 cm
2
back = 600 cm
right side = 500 cm
left side = 500 cm
10.
2
2
d)
lid of box = top side:
25 cm  30 cm
e)
2 950 cm
a)
1 hexagon;
6 rectangles
b)
Teacher to check.
c)
2
520 + [6  (10  20)]
= 520 + 1 200
= 1 720 cm
11.
2
a)
Volume of a right
prism = (area of
base)  height
b)
Q9: 15 000 cm
3
Q10: 10 400 cm
12.
13.
a)
3
2m
b)
7m
c)
4m
a)
No, he’s wrong –
he’s only multiplied
2 of the 3 edges,
plus all the units
must first be made
the same (0.5 m =
50 cm).
b)
Volume =
3
320 000 cm
Surface area =
2
28 800 cm
COPYRIGHT©2010JUMPMATH:NOTTOBECOPIED
14.
15.
a)
Teacher to check.
b)
Width = 4 cm
c)
Surface area
2
= 94 cm
Be sure to make all the
units the same first.
Volume = 510 000 cm
3
= 0.51 m
3
Surface area = 45 800 cm
2
= 4.58 m
2
AnswerKeysforAPBook7.2
U‐13