Nmne
Date
WS - Fun with Lateral Area and Surface Area ©
_
_
Pd
Solve each of the following problems. Be sure to show all work (including substitutions)
because you will need to do so on the test to review full credit.
1. Find the length of a lateral edge of a cube if the surface area is 96 ft2.
<0
0::.9<0
o
;:..I~
e ::. 4
r
2. The height a square-based right prism is four times the length of the base and the surface area
of the prism is 450 cm2. Find the dimensions of the prism.
'
x.::Sc:..~
P=L;)(
LA~
,
p~::'i)( ( 4 x') ~ 16 x
'2.
2.
,'.....,...'
'B, ~ ....
~
2
=-4~p,
SA=-\8.X
"" " ''2.
.
'2..
~ :;lS
\b~+2'"
2
=
3. The radius of the base of a ~.
cone is 12 m and height is 9 m. Find the lateral area and surface
area of the cone.
"
,
LA:
~ (2 ~1D\ 5" =-
,~O 'ii
\3= ,4t+"
4. A pyramid has a rectangular base that is 14 em xt 2 em. The lateral edges are congruent and
have a length of 10 cm. Find the surface area of the pyramid.
1-2
,0 ~~,:.
+- {
20
=-\O~-h,-r
~::
~ide ~
{~::. 5\
~::-"f5\
\0.
L f\
\,\
-=. ~ (
~ :: \"2- (\Uc)
=\~
\ (\~) (is() ~1 is)
= iL\2.)(g»
:.:-~g)
'"1'\5\') .\- d-ll.\-~)
\ l\ .~~\
-4-
q6
SA:;. ~~'4 + \L\'ffi
&;
5. A cylinder and a cone have congruent bases with radius of 10m. Both have a height of 24 m.
What is the difference in their total areas?
LA;:: ~o'\t
(2.\.\)
.c
z: \0011
x (
201\)
"2.(0)
-= a <0 0 1T
",..1("
':.. 4:<i?OT
~
\ (
LI1= 2.
fO ~
1 00 11
Ie!
S A= 3~
D"
I
I
7. Find the lateral area of this right prism.
p ::5-\-\3+ 1 ;- lo4
L Pt -;. .,
\q
(PC q') ~ (p s L\
'~
+ b t 7 of I~ -;:.1~
u15
8. Find the surface area of the problem 7's prism.
~
::
~(\~)
4-
SA- ::. {p~4
loC'~)
= ~5 +
11'4 -=- \ -, :~,
'2.
-\-"~S~ ::. 10'+ d- U
Answers to Fun with Lateral Area and Surface Area
1. 4 feet
2. length and width are 5 em.; height is 20 em.
3. LA = 1801t, SA = 3241t
4.
5.
6.
7.
8.
SA=~14J5i
3201t m2
~("Lt
8 feet
684 sq. units
1042 sq. units
em2