Now, tell me what the concept is:
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1 In silence, look at the following images… please do not discuss your ideas until you are asked to share.
description
In silence, look at the following images… please do not discuss your ideas until you are asked to share. Now, tell me what the concept is:. Pyramids! (you guys are so smart… now try another one…) (Please remember to stay quiet until I ask you to share what you think.). - PowerPoint PPT Presentation
Transcript of Now, tell me what the concept is:
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In silence, look at the following images… please do not discuss your ideas until you are asked to share.
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Now, tell me what the concept is:
Pyramids!
(you guys are so smart…now try another one…)
(Please remember to stay quiet until I ask you to share what you think.)
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Now, tell me what the concept is:
Cones!
(so smart again…I knew you could do it.)
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Mr. OwhToday isToday is: Tuesday, February 13: Tuesday, February 13thth, 2007, 2007
Lesson 12.3 – Surface Area of Pyramids & Lesson 12.3 – Surface Area of Pyramids & ConesCones
•NC 27A, 27B, 28A, 28B NC 27A, 27B, 28A, 28B
AnnouncementsAnnouncements::• Quiz for 12.1 – 12.3 is this Thursday (2/15)• You will need a calculator for this chapter
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Lesson 12.3 – Surface Areas of Pyramids & Lesson 12.3 – Surface Areas of Pyramids & ConesCones• Today’s Objectives:
Find the surface area of a pyramid.Find the surface area of a cone.
• Today’s Key Terms: pyramid, regular pyramid, slant height, lateral face, cone, circular cone, right cone, lateral surface
• Materials Needed Today:notebook, geometer/ruler, calculator
• Today’s Geometry Standard: 8, 9
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Hexagonal Pyramid ABCDEFHexagonal Pyramid ABCDEF
> V is the vertex of the pyramid and ABCDEF is the base.> Altitude is the segment from the vertex to the base (h) > Lateral faces are the six triangular faces (ex. VBC)
> are all lateral edges.
V
EFA
B CD
h
O
s
, , ,B A F EV V V V V, D,VC
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1) The base is a regular polygon.
2) All the lateral edges are congruent.
3) All the lateral faces are ≅ isosceles ’s.
4) The height of a lateral face is the
slant height of the pyramid (denoted s).
5) The altitude is the height.
6) The altitude meets the base at its center.
Regular pyramid properties:
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Lateral Area (LA) of a Regular Pyramid: is the area of just the “sides”
LA = ½Ps
NC 27A: theorem
P = Perimeter of the Bases = slant height
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Surface Area (SA) of a Regular Pyramid: is the total area of the “bottom” + all “sides”
SA = B + LA
NC 27B: theorem
B = area of the Base (formula depends on shape)
P = Perimeter of the Bases = slant height
(½Ps)
(area of all the “sides”)
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Example 1: Find the lateral area & surface area. The base is a regular polygon. Answer in both exact form & to the nearest hundredth.
LA= ½ ps P=8+8+8 P=24LA= ½ (24)(12)LA=144cm²
SA = B + LA
12cm
8cm
8
sB
2 3
4
28 3
4
64 3
4
SA = 16 3 144 171.71cm²
16 3
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Example 2: Find the lateral area & surface area. Answer in both exact form & to the nearest hundredth.
LA = ½ ps P =15+15+15+15 P =60LA = ½ (60)(18)LA = 540in²
SA = B + LA B = s² B = (15)² B = 225SA = 225 + 540SA = 765in²
18in
1515in
15
15
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ConeCone
A cone has a vertex and a circular base. The axis is the segment that joins the vertex to
the center of the base. If the axis is to the base, then the cone is a
right cone.
Axis
slant height
h
vertex
r
Altitude or height
vertex
Right Cone Oblique Cone
Axis
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1) The base is circular.
2) The altitude is the height.
3) The slant height (denoted s) is the
distance between the vertex and a point
on the base edge.
4) If the height is to the base, then the cone is a right cone.
5) The altitude meets the base at its center.
Right cone properties:
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Lateral Area (LA) of a Right Cone: is the area of just the “sides”
LA = ½(2r)s or
LA = rs
NC 28A: theorem
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Surface Area (SA) of a Right Cone: is the total area of the “bottom” + all “sides”
SA = r² + LA
NC 28B: theorem
(rs)
r = radius of the Bases = slant height
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Example 3: Find the lateral area and surface area of a right cone whose base radius is 8cm and slant height of 15cm.
Answer in both exact form & to the nearest hundredth.
TIP: Try drawing the figure first
Answers:a)
b)
LA cm 2120
SA cm 2184 . cm 2578 05
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Example 4: Find the lateral area and surface area of the following:
SA LB A
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6LA sr ss s 2 2 24 6
s 2 24 6 52
LA sr ( ) 4 2 13
2 84 13
16 36
unit. 2140 88
2 13
8 13
6 81 13
HW G1 #10 (Due wed 2/15)HW G1 #10 (Due wed 2/15)Page 738 {3–25 odd, 32–35}Page 738 {3–25 odd, 32–35}TIPTIP: Use Pythagorean Theorem for {15 & 21} to find : Use Pythagorean Theorem for {15 & 21} to find slant height & Write ALL answers in slant height & Write ALL answers in exact formexact form too. too.
COPY FIGURES !!!COPY FIGURES !!!
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Example 5: Find the surface area of a hexagonal pyramid with a lateral edge of 13cm and a base edge of 10cm.
SA LB A
SA 150 3 360
cmSA . 2619 81
LA360B 150 3
