Sec. 11 – 2 Sec. 11 – 2 Surface Area of Prisms Surface Area of Prisms & Cylinders & Cylinders Objectives: Objectives: 1) To find the surface area of a 1) To find the surface area of a prism. prism. 2) To find the surface area of a 2) To find the surface area of a cylinder. cylinder.
Sec. 11 – 2 Surface Area of Prisms & Cylinders Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder.
Jan 21, 2016
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Sec. 11 – 2 Sec. 11 – 2 Surface Area of Prisms Surface Area of Prisms & Cylinders& Cylinders
Objectives: Objectives: 1) To find the surface area of a prism.1) To find the surface area of a prism.2) To find the surface area of a cylinder.2) To find the surface area of a cylinder.
I. Surface Area of a I. Surface Area of a PrismPrism
PrismPrism – Is a polyhedron w/ exactly 2 – Is a polyhedron w/ exactly 2 , // , // faces, called bases.faces, called bases. Name it by the shape of its 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 Right Prisms vs Oblique PrismsPrisms
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 Ex.1: Use the net to find the Surface Area of the rectangular Prism.Area of the rectangular Prism.
5cm
3cm
4cm
3 4 3
4
3
5
3
Area of Bases: A = l•w
12
12
2 different Lats: A = l•w
15 20 15 20
SA = LA + BA
= 70cm2 + 24cm2
= 94cm2
Ex.2: Find the total surface area of the Ex.2: Find the total surface area of the following triangular prism.following triangular prism.
6cm
5cm
5cm
12cm
LA = l•w
(5 x 12) = 60cm2
(5 x 12) = 60cm2
(6 x 12) = 72cm2
BA = BA = ½bh½bh
= ½(6)(4)= ½(6)(4)
= 12cm= 12cm22
x 2x 2
24cm24cm22
5
3
h
a2 + b2 = c2
h2 + 32 = 52
h = 4
6
192cm2
SA = LA + BA
= 192cm2 + 24cm2
= 216cm2
Ex.2: Find the total surface area of Ex.2: Find the total surface area of the following regular hexagonal prism.the following regular hexagonal prism.
LA = l•w
(10 x 12) = 120m2
x 6
BA = ½ap
= ½(8.7)(60)
= 260m2
x 2
520m2
720m2
SA = LA + BA
= 720m2 + 520m2
= 1240m2
10m
12m
10
5
30°
a
Tan 30 = 5/a
.577 = 5/a
a = 8.7
II. Finding Surface Area of a CylinderII. Finding Surface Area of a Cylinder
CylinderCylinder Has 2 Has 2 , // bases, // bases Base Base → → CircleCircle
C = 2C = 2ππrr A = A = ππrr22
height
r
r
h
r
Net of a Net of a Cylinder:Cylinder:
LA is just a Rectangle!
LA = 2rh
rBA = r2
Area of a circle
Circumference of the circle
SA = LA + 2BA
Ex.4: SA of a right cylinderEx.4: SA of a right cylinder
6ft
9ft
LA = 2rh
= 2(6)(9)
= 108ft2
= 339.3ft2
Area of Base
BA = r2
= (6)2
= 36ft2
x 2
= 72ft2
= 226.2 ft2
SA = LA + BA
= 339.3ft2 + 226.2ft2
= 565.5ft2
EXAMPLE: Round to the nearest TENTH.
Top or bottom circle
A = πr²
A = π(3.1)²
A = π(9.61)
A = 30.2
Rectangle
C = length
C = π d
C = π(6.2)
C = 19.5
Now the area
A = lw
A = 19.5(12)
A = 234 Now add:
30.2 + 30.2 + 234 =
SA = 294.4 in²
Practice:Practice:
WorksheetWorksheet
What did I learn today??What did I learn today??
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