Surface Area of Prisms
-
REVIEW: WORKING WITH AREAS OF TWO-DIMENSIONAL FIGURES
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Page 2
BUM*
Calculate the area of each figure.
a)
9 5..a4
, L./91z
4.5 cm
C fri^
6.8 cm
12.8 cm
5,1
‘fiSen
3.1 in
Page 3-
Example 2
Find the area of the following figure.
6.2 cm
3.1cm
6.8 an
t 31
o
:At
1.2 ,
13.4 cm
12.6 em
C"
„ i 12
Page 4
NEW SKILLS: WORKING WITH THE SURFACE AREA OF PRISMS
prism is a three-dimensional object
• ends, called bases, that are congruent and parallel, and
• sides, called lateral faces, that are parallelograms,
The prism is a right prism if the sides arc perpendicular t
bases. The lateralaces
will be rectangles.
If the lateral faces are not perpendicularthe base, it is an oblique prism and the sides
will be parallelograms.
A prism named by the shape of its base and Whether it is right or oblique.
Name the following prisms..
B)
Page 5
NEW SKILLS: WORKING WITH NETS
A net is a two-dimensional pattern that can be folded to
shape. Think of a pizza box: it is made up of one piece
rm a three-dimensional
rdboard, folded into the
shape of a right rectangular prism.
The su
a of a prism is the area that it would take up if it were laid. out t,
in its net.
Example 4
this right pet
zs. nal prism were made [rem one piece
piece of cardboard look like?
aid the
Page 6
Exaniple 5.
Find the surface area of the right rectangular prism given below.
t--L9 x2__
A 9 y 3j x2_
3t9c
11,yr
Latvia
tY
Find the surface area of this figure.
F
55cm
050,01--
Page 7
Kareem has been hired to paint the walls and ceiling of a living room in a house. The
room is 225 feet long, 13.5 feet wide, and 8.5 feet high. There is one window that is
10.5 feet by 6 fret, two windows that are 33 feet by 2.5 fret, and two doors that are 23
feet by 8 feet.
5.25 11 •
a) What surface area must he paint?
b) One gallon of paint covers approximately 255 sq. ft. How many gallons will he
have to buy? 3.. tk t-- 4 34(toKs
c) If paint costs $55.40 per gallon and he wants to make a profit of about $225.00,
how much should he chug to paint the room?
sob =
.5; ego xt44gDi 60
'
,I 1
,2AC
11.31;-)3)c x [;),s-
Al
Iv-05
2 S
4
gc5 01,2‘
111,2_5
"tett
qI5, / 5
1 ° _ widnus c,
95
9)3.1.5
Page 8
- Surface Area of Pyramids Cylinders, Spheres, & Cones
RE VIE WORKING WITH CIRCLES
In this Se Uon, you s1U nted to Lalculatehe circumference a
Example 1
Find the area of the following figure.
11Th cm
be area o tries.
Page 9
NEW SKILLS: WORKING WITH THE SURFACE AREA OF CYLINDER
A cylinder is like a pfism but it has circular bases. To find the surface area, you have
to find the area of the two circles and the area between them. If you draw a net of a
cylinder, you Will find that it is made up of a rectangle and two circles. The length of the
rectangle will be the circumference of the circle, and the width wilt be the height of the
cylinder.
circumference C
Example 2
80m
Find the surface area of a cylinder that has a radius of 90 mm and a height of 300 rum.
SOLUTION
cd__.
=IT )( 60
7
90 mm
5 0;,1/44C
A
(3u
2C`l'ite,±1
x ci-viis
-----__50a9 3
I
771-1- S.
-
5 "‘.' yosny
iyiv),
•
2_
r 22kS 3 91
i-nwt
Page 10
NEW SKILLS: WORKING WITH THE SURFACE AREA OF PYRAMIDS
A pyramid is a three-dimensional object with a polygonal base and lateral sides that are
triangles. The triangles meet at a point, called the apex. In a right pyramid, die apex is
aligned above the centre of the base.
The net of a pyramid will consist of the base plus as many triangles as there are sides to
the base.
Example
Find the surface area of the square-based pyramid below.
Page 11
**011447.
Fmd the surface area of the square-based pyramid.
bLtn
iL i!
.t
/80
v
ito
NEW SKILLS: WORKING WITH THE SURFACE AREA OF CONES
A cone is like a pyramid, but it has a circular base. The net of a cone is a sector of a large
circle, and the circular base of the cone.
The surface area of the lateral area of the cone (the area not including the base] can be
calculated using this formula, where r is the radius of the circular base ends is the slant
height of the lateral face:
mfr
,
4 stow
_
Page 12
Find the surface area of a cone that has a radius of 12 feet and a slant height 01 15 feet.
ifrS t
\I
flY
CI y 124-
st
59
1
L
Example 6
Find the surface area of the cone.
9.6 cm
Sfr=
Vr5
r -Wr y
t
c- g
g.0(0.(0
t
2-19 coma-
r'Le
t
13-
la
11.82-
Page 13
NEW SKILLS: WORKING WITH THE SURFACE AREA OF SPHERES
A sphere is like a ball. All points on the sphere are equidistant (of equal distance) from
the centre. It is not possible to draw a net of a sphere. The formula for a sphere's surface
area depends only on the radius and .7r. The formula for the surface area of a sphere is:
(SA = 4xr
:;Examplel..e.
A ball has a surface area of approximately 9900 cm!. What Is its radius?
a
990o= Lirri-L
4ff
r
••••
91°D
• -K 1("---
JEXaMpla.S.:
Find the surface area of the composite figure.
11- v. silo".
fi-vecA
C.6
.4k
$
bay9.3cm
/87. 96
ot A 4
k
%,,;1-kowt 1.4ae
ft r 5
112cm
r 1.1
f
gje
Lic 93
.2 3 3i 15 9 eivk taAi
C
"CL
•- 112- 5 C I
ttt
3
32 '
2.1
Page 14