11­3 SA of pyramids and cones 2011
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Find the surface area of pyramids and cones.
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March 31, 2011
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11­3 SA of pyramids and cones 2011
March 31, 2011
Warm­Up
1. Draw the net of the pyramid.
2. Draw the net of the cone.
base
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11­3 SA of pyramids and cones 2011
base
March 31, 2011
To find the surface area of a pyramid, find the area of its base and then add the area of its faces.
SA = Area of Base + Area of Faces
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11­3 SA of pyramids and cones 2011
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Find the surface area of this pyramid.
First, label the net.
6 ft.
4 ft. 6 ft.
6 ft.
6 ft.
6 ft.
How are we going to find the height of the triangles?
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11­3 SA of pyramids and cones 2011
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The green line is the height of the triangle.
4 ft. Use the Pythagorean Theorem to find the length.
2
2
2
a + b = c
2
2
2
3 + 4 = c
6 ft.
9 + 16 = c 2
25 = c 2
25 = c 2
5 = c
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11­3 SA of pyramids and cones 2011
March 31, 2011
1. Find the Area of the Base.
2. Find the Area of the Faces.
5
6 ft.
5
6 ft.
6 ft.
6 ft.
5
3. Add them together to get the Surface Area.
5
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11­3 SA of pyramids and cones 2011
March 31, 2011
To find the surface area of a cone, first make a "net".
s
NET
r
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11­3 SA of pyramids and cones 2011
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You do NOT need to write down the process to derive the following formula. You just need to watch and ask questions if you do not understand.
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11­3 SA of pyramids and cones 2011
s
r
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Find the area of each piece and then add them together.
Area of the Circle:
A = r2
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11­3 SA of pyramids and cones 2011
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Area of the sector:
s
First, cut the sector into many triangles.
r
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11­3 SA of pyramids and cones 2011
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Area of the sector:
s
First, cut the sector into many triangles.
If we find the area of the triangles, we will have the area of the sector!
r
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11­3 SA of pyramids and cones 2011
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Area of the sector:
s
First, cut the sector into many triangles.
If we find the area of the triangles, we will have the area of the sector!
r
A = b h
2
The base of ALL the triangles together is the Circumference of the circle!
The height of all the triangles is s.
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11­3 SA of pyramids and cones 2011
March 31, 2011
Area of the sector:
s
First, cut the sector into many triangles.
If we find the area of the triangles, we will have the area of the sector!
r
A = b h
2
The base of ALL the triangles together is the Circumference of the circle!
The height of all the triangles is s.
A = C s
2
C = 2 r
A = 2 rs
2
Area of the Sector
A = rs
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11­3 SA of pyramids and cones 2011
s
March 31, 2011
Now, add the two areas together!
A = r2 + rs
A = rs
Factor out a common term:
r
A = r2
A = r(r + s)
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This is the part you need to write down:
The surface area of a cone is:
A = r (r + s)
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11­3 SA of pyramids and cones 2011
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Let's try one! Find the surface area of this cone.
Step 1: Find "s".
Step 2: Use the formula to find the surface area.
SA = r(r + s)
h = 5 in.
r = 2 in.
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Homework
p. 620
#1-3, 8-10, 18-20
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11­3 SA of pyramids and cones 2011
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