12.3 surface area of a pyramids and cones
DESCRIPTION
12.3 Surface Area of a Pyramids and Cones. Slant Height ( l ). Definition of a Regular Pyramids. A regular pyramid is a pyramid whose base is a regular polygon and whose vertex forms a segment with the center of the polygon perpendicular to its plane. Part of a Pyramid. - PowerPoint PPT PresentationTRANSCRIPT
12.3 Surface Area of a Pyramids and Cones
Slant Height ( l )
Definition of a Regular Pyramids
A regular pyramid is a pyramid whose base is a regular polygon and whose vertex forms a segment with the center of the polygon perpendicular to its plane.
Part of a Pyramid
h is Height from base to vertexl is Slant height, The height of the triangle
edgelaterial
edgeBase
s21
Theorem
Surface Area of a Regular Pyramid
B is for base AreaP is for perimeterl is for Slant height
PBAS 2/1..
Surface Area of a Regular Pyramid
Let r = 3; h = 4Find the Perimeter
r is half the base edge
PBAS 2/1..
Surface Area of a Regular Pyramid
Let r = 3; h = 4Find the Perimeter
r is half the base edgeBase edge is 2(3) = 6Square perimeter 4(6) = 24P = 24
PBAS 2/1..
Surface Area of a Regular Pyramid
Let r = 3; h = 4 ; P = 24Find the Base Area
PBAS )2/1(..
Surface Area of a Regular Pyramid
Let r = 3; h = 4 ; P = 24 ; B = 36Find the Base Area
Base edge is 6Base Area = (6)2
B = 36
PBAS )2/1(..
Surface Area of a Regular Pyramid
Let r = 3; h = 4 ; P = 24 ; B = 36Find the Slant Height l
Right Triangle
PBAS )2/1(..
Surface Area of a Regular Pyramid
Let r = 3; h = 4 ; P = 24 ; B = 36 ; l = 5Find the Slant Height l
Right Triangle side legs 3 and 432 + 42 = l 2
9 + 16 = 25 = l 2
l = 5
PBAS )2/1(..
Surface Area of a Regular Pyramid
Let r = 3; h = 4 ; P = 24 ; B = 36 ; l = 5 PBAS )2/1(..
96..120)2/1(36..
524)2/1(36..
ASASAS
Surface Area of a Regular Pyramid
Let r = 4; h = ; P = 24 ; B = ; l = 9Find the Base and Perimeter
PBAS )2/1(..
4
Surface Area of a Regular Pyramid
Let r = 4; h = ; P = 24 ; B = ; l = 9Find the Base and Perimeter
PBAS )2/1(..
4
24)4(6
324346..
43416. 2
PAB
AB
324
Surface Area of a Regular Pyramid
Let r = 4; h = ; P = 24 ; B = ; l = 9Find the Surface Area
PBAS )2/1(..324
Surface Area of a Regular Pyramid
Let r = 4; h = ; P = 24 ; B = ; l = 9Find the Surface Area
PBAS )2/1(..324
6.149..
108324..
924)2/1(324..
AS
AS
AS
Surface of a Cone
Finding the Base is Easier, since it is a circle.
rrAS 2..
Surface of a Cone
Finding the Surface Area.r = 5, h = 12
rrAS 2..
Surface of a Cone
Finding the Surface Area.r = 5, h = 12; need l
rrAS 2..
Surface of a Cone
Finding the Surface Area.r = 5, h = 12; need l
rrAS 2..
13169
14425
1252
222
Surface of a Cone
Finding the Surface Area.r = 5, h = 12; need l
rrAS 2..
90..
6525..
1355.. 2
AS
AS
AS
Homework
Page 738-741 #15 – 43 odd
Homework
Page 738-741 # 14 - 38 even,
44 - 46