Sec. 11 – 2 Surface Area of Prisms & Cylinders
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Transcript Sec. 11 – 2 Surface Area of Prisms & Cylinders
Surface Area
of
Prisms & Cylinders
Objectives:
1) To find the surface area of a prism.
2) To find the surface area of a cylinder.
I. Surface Area of a Prism
Prism – Is a polyhedron with exactly 2 ,
// faces, called bases.
Name it by the shape of its bases.
Bases are Rectangles:
Lateral Faces – All faces that
are not bases. (Sides)
Right Prisms vs Oblique Prisms
Right Prism – Edges
are Altitudes.
Oblique Prism
Lateral Area – The sum of the areas of the
lateral faces (sides)
• Right Prisms - Lateral Faces are Rectangles
A = l•w
Base Area – The sum of the areas
of the 2 bases
• Rectangle: A = l•w
• Triangle: A = ½bh
• Polygon: A = ½bh
Total Surface Area = Lateral Area + Base Area
Ex.1: Use the net to find the Surface Area of the rectangular Prism.
Area of Bases: A = l•w
2 different Lats: A = l•w
4
5cm
3cm
3
4
3
15
20
15
12
3
20
5
4cm
SA = LA + Area of Bases
= 70cm2 + 24cm2
= 94cm2
12
3
Ex.2: Find the total surface area of the
following triangular prism.
5cm
LA = l•w (Area of Sides)
(5 x 12) = 60cm2
5cm
(5 x 12) = 60cm2
12cm
(6 x 12) = 72cm2
6cm
192cm2
Area of Triangle
BA = ½bh
= ½(6)(4)
= 12cm2
x2
24cm2
5
a2 + b2 = c2
h2
+
32 =
h=4
52
SA = LA + BA
h
= 192cm2 + 24cm2
6
3
= 216cm2
Ex.2: Find the total surface area of the
following regular hexagonal prism.
LA = l•w
(10 x 12) = 120m2
12m
x 6
720m2
BA = ½ap
= ½(8.7)(60)
= 260m2
x2
520m2
10
30°
a
10m
SA = LA + BA
5
Tan 30 = 5/a
= 720m2 + 520m2
.577 = 5/a
= 1240m2
a = 8.7
II. Finding Surface Area of a Cylinder
Cylinder
Has 2 , // bases
Base → Circle
r
C = 2πr
A = πr2
height
r
h
r
Net of a
Cylinder:
LA is just a Rectangle!
LA = 2rh
Area of a circle
BA = r2
r
Circumference of the circle
SA = LA + 2BA
Ex.4: SA of a right cylinder
LA = 2rh
6ft
9ft
= 2(6)(9)
Area of Base
= 108ft2
BA = r2
= 339.3ft2
= (6)2
= 36ft2
x2
SA = LA + BA
= 72ft2
= 339.3ft2 + 226.2ft2
= 226.2 ft2
= 565.5ft2
What did I learn today??
Find the area of the lateral sides first!!
Usually rectangles
Be careful, the rectangles are not always the
same size.
Second, find the area of the Base
Rectangle, Triangle, Polygon, or a Circle
There are always 2 bases in prisms.
Multiply by 2!