W \ ,Q.
ChO(l~
• GEOMETRY A
f1t'SWif
NAME:
DATE:
REVIEW PACKET TEST CH 12
to ;;:::~2
--------------_
\~
~ If' ==- ~_]
3) The cube has a volume of 64a6 cubic centimeters.
Find AB in terms of a.
B
A82
(L\az)~-+ (L\C\~'J2)?-
!'r0-
\!ooL-l
+
x
320Y
fAd\::~oY --D(- A-B -=-yJ3a.0
4) A right, square pyramid has lateral edges that measure 8 in. The lateral faces of the pyramid are
equilateral triangles,. Find the total surface area and volume of the solid.
1St+ = (2) -+
1?L
;; ll-i +~
3-( j/,)l4J3 ')
v-==- ~
(f»~)(~')
~l CbC\)LL.\J2)
3
CoL{+-Gt{~
\V==?~J2y'2. +-h2--=-{lfJ3Y
Ib+0~=Y~
h~=~
h -=- YJi
5) A cube has a volume of 30.
of the cube and the vertex
the pyramid.
A pyramid is "inscribed" in the cube. The base of the pyramid is the face
f the pyramid is at the midpoint of the opposite face. Find the v~lume of
'"v
\fCUBe"
.' 'f.." , 'A
'/-...~ :=:-
'f.. ~
::..--~=~---~
~~
-=
'f-...
2>
\I ~\(\2:::: .3
\ l/\,eu~ '\)
r
II
\J
~a
~ ~ (30)
3J 3a
\ V Pvo- "=' \ 0 ]
t
c,W\UL
Bo.~
c{.-
ne>s~
o.('e-su.~\\.~
Qhe figure shown below is r tated
about the dotted line. Determine the 3-dimensional figure that is
ind the volume and total surface area of this figure.
created by this rotation.
'/...
-
y... +-2.D
'5
I
0'2.
I
zh
3
1\" \t- '3 lTf
,,:=.
\S
==-
J-
\5y.=5
jlT(
V-:=-
6t
V:::::-
0
_r::"
f3
3
,.-;:;
?£.bJ3
~~
\+ -=\ U,J3
~
\2~
S
~
T3~l\ii'2
3=
:.;~~~.;:
~
11
tc
-"TIC.t
-n(\5}'2- +T\(5V",-\--'\i(lS)(:e)-rr(sx.to)
!'\ \lS
\ 5 :::\<.
5
-
0 Y~(5E)
\\2E5-{6 -3
-
r:
n-( \5)2( \~)
-=- 22'"j
lOr:::.
fB)
\T
,
-=
-+ 25IT -t'tEihll" ~TI
>" \
I
the volume and total s rface area 0 the following non-right (oblique), circular cylinder. The slant
is 5 and the diameter 0 the base is 4.
~ind
~ght
\f "" "T(,2h
= "l2-f'-.
,SA -=:-1lTr~ + L,,~2-:::-2--rt ( 2-)( {)(I-~ -+
ll~~
\-----
.'"
1
~ =: \ IOM=
V]
___
f
4
A~
_
\
8) Find the total surface area and volume of the right, regular hexagonal pyramid. The base edges are 6
3M.
PL
and the height is
(SA- == ~ -\-
-i =- 5YJ3 -+ ~ (jCo ) ( \2") ~
2 \~-\-5l-4J3
= 2-lb-\5'{5 ]
~
V = ~ ~h
= ~ (5'\J3J(3J\3)
. \V
=--
JS'-i fi' ]
6
t
(3J3 y--t (3 [B):l.:.
2"1- -+- Ir?-
L
= P"-'2-
1. -; 12..
9) Find the total surface area and volume of the right prism.
B:=:- 0
b:>
+
B
lSPr
-=
26
+-
== Lf-\Ji+ ~'(4E)('-{~2')
:=-
Lj4-f2- + Ito
p,~ -::::2.[
-= <6~S"i--\_
\I
\f -=
-=:-200
~l
~
L.\'2G
1
~fz..
i-~-\'(o-P-:?--+-2-2. 0\-'] .,..
\'")(\L\ )
14 in
+ \.l '2["2-
J'2- -\- ~s2..
~
(l.j c{ b-r
'"
G) (14)
+ ( 30 + % 2.
~'-{ Ii +H:»
••
II •
I
3
10) The height of a cylinder is three times its radius. The volume of the cylinder is 1627Z' m
total surface area' of the cylinder. (~~
\a \'\j.al(~-\- \\.J.J.I'\C\f.ed-fu)
f'-----
\J ::::If\"2 h
'" =- 1\ \" (3('")
\1 := '3 -m'"' 3>
2>
~
l' -:::::
3 fX'
\ 'S
\Br
I
\~
'3
-=(~
Find the
A- -::::-2 "r2- +L\i r h
=- 2.: ( 3.91-0.
1t
'2
.
~ ") 2.
JS~ ::::\\Y.2<1L\\T
(j)-
\
3SQ,O=r
+ 2 n(3 '"77G<l)
( II. ~-3q3)
11) A cube with edge 8 cm ha one cylindrical hole drilled through the middle of the cube that has a
diameter of 6 cm. Find the to 01 surface area and volume of the cylinder.
TSA ;;:..l'SflrPiLISl'A
/ :~
::::.2-8+ Ph
I
)
~ \?-~ -4-
\~
\f
V ~\2.\$\\A
1?> =.
'2\"\r\-J
(3)Z+-L\\(3J(?S)
"
_ \<6" k l-\ l$'\\
25G
-t 30"
V~\,
::::.8\1 - \\ r'2 h
-==-
IV
~
_2(1\{.2-)-\-
J
= 3%'\
=~~ind
L31\- c..'(,-"
::::'2-(~<.t) +-- 32( 'S) -
I
I
+
2 Q I~c.\es
2
..
I.
-
-
tD4('i)} --n[3}~(&)
= 51J- -
-=r2-D .
the lateral surface a eo, total surface area, and vo,lumeof a pentagonal
a bose perimeter of 60 i .
~ <>." =
\~ =
-i.('I %) (",) \
\'30'6
J~.
(2ACA.\0C\
L- ''is '"
+-v
~\ei\-
= 1(i(JI'11, ~
pL
= -.k (,,0lllo'\
\ \ LS~
'TS p..
-:=0
?,n3
~I<'d~(k-\'~f\")
\'\
]
-=- B + l-SA
-::=-
\30,~ --r =32-7 . 3>
\TS~
::=
L\5$5. \
1
~----.
i\\ifO'mlc\
. . with a height of 10
•
Name
'.
•
_
Class
Date_~
_
Additional Practice 23
Use after Section 12.4
SURFACE AREA
AND VOLUME
Problem Set A
1 Find the volume of each solid.
a
b
c
la
12
I
lb
"1
eJ
lc
2
Right prism
14
3
4
=
Y[
Y5 J3"
1\
(5)'2-( \ 2-)
~(")~J(
\2)
= (~2-~)(~)
Right prism
m
Find.the volume
and the total area.
29
=-
6
12
Right circular cylinder
360"
2
2TIJ
3 30
9
Find the volume and
the total surface area.
3
Find the volume of
the prismatic solid.
4
-==-v
::::-T~
Problem Set B
GJ ba
5a
Find the volume of each right prism.
Find the total area of each solid.
a
5b
T9~-=-
,sA =-
G\iO<O
'&X)
v-=- \b1D
\j ::::-i0'20
b
6
24
~
25
t;\ A trapezoidal
D
••
darn is to be
built across a river.
a Find the volume of cement
needed to form it.
b Find the total area of the darn.
2
10
236
Additional Practice
23
6a
IO~Q
6b
q\'2(continues)
Copyright
@
McDougal. Littell & Company
Name
•
•
Class
SURFAC
AND
Va
Date
Additional Practice 24
AREA
UME
Use after Section 12.5
i
Problem Set A
1 Find the volum
of the pyramid.
The base is a sq are.
L(3"
1
,
'1
2
4J
Find the volum of the cone
whose base is a ircle with
radius 5 and wh se height is 18.
i
I
"1
!
2
1£:50 \T
Problem Set B
3
•
r
4
j
;
Find the volume of the tower.
It has a total hei ht of 12 m, a
height up to the oof of 10 m,
and the base is a equilateral
triangle with as' de of 4 m.
A pyramid with
on top of a cube
12
10
\2-1>8
3
3
eight 3 is mounted
ith an edge of 8.
\
a
i
b
I
5
J
ii
f,:
•
6
238
Find the total volume
contained in he solid.
Find the total surface area.
Find the ratio of e volumes
of a cone and a c linder that
have the same b e and height.
If point Q has co rdinates
(4, 4, 9) and the b se of the
cone is tangent to the x- and
y-axes, find the v lume of
the.cone.
Additional
Practi e 24
@
4a
5?-b
4b
l{oo
5
3
z Q
6
Copyright
@
l-(f)1T
McDougal, Littell
&
Company