Transcript WARM-UP

WARM-UP
Find the volume of each solid.
8
6
12
12
13
18 19
12
10
10
SURFACE AREA
PRISMS
AND
CYLINDERS
DEFINITIONS
Prism: 3-D shape with two congruent
bases.
Surface Area: the sum of the areas of
all the surfaces that bound the solid
PRISMS
To understand surface area it helps to look at the
“net” of the shape.
10m
8m
6m
8m
10m
10m
6m
8m
6m
6m
PRISMS
To find SA, you can just calculate
the area of all the individual
rectangles and add.
10(8)(2)=160
10(6)(2)=120
8(6)(2) = 96
SA = 376 m2
10m
10m
8m
6m
8m
6m
6m
PRISMS
There is an alternative…
5
4
3
5
5
6
SA
SA
SA
SA
=
=
=
=
6
2B + Ph
2(0.5)(3)(4)+12(6)
12 + 72
84 sq. units
3
Notice the middle is one
4 big rectangle
4
The height is the
same as the prism,
and the length is
6 the same as the
perimeter of the
base triangle.
SA = area of two
bases + area of big
rectangle…
PRISM - EXAMPLE
1. Find the surface area of the rectangular prism.
Method 1:
7(5)(2) = 70
5
9(7)(2) = 126
9(5)(2) = 90
7
SA = 286 sq. units
Method 2:
SA = 2B + Ph
9
SA = 2(5)(7)+24(9)
SA = 70 + 216
SA = 286 sq. units
PRISM - EXAMPLE
2. Find the surface area of the triangular prism.
13
Method 1:
0.5(12)(5)(2) = 60
5
12
5(20) = 100
12(20) = 240
13(20) = 260
SA = 660 sq. units
20
Method 2:
SA = 2B + Ph
SA = 2(0.5)(5)(12) + 30(20)
SA = 60 + 600
SA = 660 sq. units
CYLINDERS
There is one major difference between prisms and
cylinders.
With prisms, SA can be found using two different
methods: break it up or use the formula: 2B+Ph
With cylinders there is not a choice, the formula
must be used.
CYLINDERS
Let’s look at the “net” of a cylinder.
8
pd = p(16)
8
14
14
16
CYLINDERS
8
pd = p(16)
Use the formula for a
prism: 2B+Ph. There
is no perimeter, but
there is
circumference.
The specific formula
for SA of cylinder is…
14
16
SA = 2pr2 + pdh
EXAMPLE-CYLINDER
1. Find the surface area of the cylinder
SA = 2pr2 + pdh
8
SA = 2p82 + p(16)(14)
SA = 128p + 224p
SA = 352p sq. units
14
(EXACT ANSWER) or
SA = 1105.28 sq.units
EXAMPLE-CYLINDER
2. Find the surface area of the cylinder
SA = 2pr2 + pdh
18
SA = 2p92 + p(18)(27)
SA = 162p + 486p
SA = 648p sq. units
27
(EXACT ANSWER) or
SA = 2034.72 sq.units