Upload
priscilla-randall
View
214
Download
0
Tags:
Embed Size (px)
Citation preview
LESSON 11.1
• I can identify and name 3-dimensional figures
• I can identify and name parts of 3-D figures (faces, bases, edges, vertices)
• I can identify the shape of cross sections of 3-D figures and find the area of the cross sections
solidflat surfaces
polygons
2parallelcongruent
2parallel congruent
1 basepoint
vertex
shape base(s)
Rectangular prism Pentagonal pyramid
Triangular prism Trapezoidal prism
Pentagonal prism Square (or rectangular) pyramid
∆ABC , ABED, BEFC,ADFC∆DEF
AB BC CA DE EF FD BE CF ADA, B, C, D, E, F
parallel basescircles
circularbase vertex
plane
circle rectangle
rectangle rectangle
44
4
square
A = bh
A = 4(4)
A = 16 un2
Isosceles triangle
A = ½ bh
A = ½ 18(12)
A = 108 cm2
triangle
A = ½ bh
A = ½ 9(6)
A = 27 un2
rectangle
A = bh
A = 10(6)
A = 60 in2
11-1 worksheet
ASSIGNMENT
LESSON 11-2
I can draw 2-d models for 3-d figures
I can surface area using nets
2 pattern
Top
Bottom
Front
Back
Left
Right
1
26
88
10
SA = square + 4 triangles
= 64 + 4 (40)
= 224 un2
7
3
5
3
55
35
SA = 6 rectangles
21
35
21
15 15
= 142 un2
7
15
48π
SA = rectangle + 2 circles
15(8π)120π + 2π(42)
+ 32π= 152π
≈ 477.52 cm2
Shape of
Lateral Faces
Number of
Lateral Faces
Number of
Bases
Shape of
Base
& Number of Sides
Number of Edges
Number of Vertices
Ex Octagonal Prism 8 2 8 24 16
1 Square
Prism 4 2 4 12 8
2 Rectangular Prism 4 2 4 12 8
3 Pentagonal
Prism 5 2 5 15 10
4 Triangular
Prism 3 2 3 9 6
Draw pictures!
Use the solids to answer the questions for each shape.
Investigation #1 - Prisms
Number of
curved surfaces
Shape of
Curved surface when
flattened
Number of
Bases
Shape of
Base
Number of curved edges
Number of apexes
(like a vertex)
8 Cylinder 1 2 2 none
9 Cone 1 1 1 1
10 Sphere 1 none none none none
11 Hemisphere 1 1 1 none
Draw pictures!
Use the solids and the nets to answer the questions for each shape.
Investigation #3 – Solids Involving Circles
Shape of
Lateral Faces
Number of
Lateral Faces
Number of
Bases
Shape of
Base
& Number of Sides
Number of Edges
Number of Vertices
Ex Pentagonal Pyramid 5 1 5 10 6
5Square
Pyramid 4 1 4 8 5
6 Octagonal
Pyramid 8 1 8 16 9
7 Triangular Pyramid 3 1 3 6 4
Draw pictures!
Use the solids to answer the questions for each shape.
Investigation #2 - Pyramids
Prisms PyramidsLateral Faces Rectangles Triangles
Bases Two matching polygons
One polygon
Edges Base edges times 3 Base edges times 2
Vertices Base vertices times 2 Base vertices +1
Name ____________ prism __________ pyramid
When the base is a circle it’s called a…
Cylinder Cone
11.1 Identify parts of 3d figuresSummarize the differences between prisms and pyramids
(name of base) (name of base)
1. Draw and label a net for the following solid. Then find the surface area.
Warm Up
8 888 8
3
3
3
3
3
3
22
22
2 2
16 1624 24
6
6
SA = 16+16+24+24+6+6 = 92 un2
11-2 worksheet
ASSIGNMENT
LESSON 11-3
I can find the volume of prisms
I can find the volumes of cylinders
V = Bh
B = area of base
V = πr2h
= π(82)
= 1120π mm3
≈ 3518.58 mm3
(17.5)
V = πr2h
= π(82)
= 1920π cm3
≈ 6031.86 cm3
(30)
V = πr2h
= π(62)
= 414π in3
≈ 1300.62 in3
(11.5)
V = πr2h
= π(3.52)
= 294π ft3
≈ 923.63 ft3
(24)
V = πr2h
24 ft
B = 1/2h(b1+b2)
= 1/2(1.5)(2 + 4)
= 4.5
V = Bh
= 4.5 (6)
= 27 cm3
B = 1/2Pa
= 1/2(36)(5.2)
= 93.6
V = Bh
= 93.6 (12)
= 1123.2 in3
B = bh
= 10(15)
= 150
V = Bh
= 150
= 1800 ft3
(12)
B = 1/2bh
= 1/2(9)(6)
= 27
V = Bh
= 27(10)
= 270 un3
V = Bh
735 = 42h42 42
17.5 cm = h
V = Bh
196 = 16B
16 16
16 = B
?
?164 in by 4 in
11-3 worksheet
ASSIGNMENT
LESSON 11-4
I can find the volume of pyramids
I can find the volume of cones
segmentvertex
base
heightlateral face
segmentvertex
perpendicularbase
V = 1/3 Bh
B = area of base
V = 1/3 πr2h
V = 1/3 πr2h
= 1/3 π(42)(7)
= 37.3π in3
≈ 117.29 in3
V = 1/3 πr2h
= 1/3 π(102)(24)
= 800π ft3
≈ 2513.27 ft3
24
V = 1/3 πr2h
= 1/3 π(62)(8)
= 96π cm3
≈ 301.59 cm3
8
r = 10
h = 12.73
V = 1/3 πr2h
= 1/3 π(102)(12.73)
= 424.3π yd3
≈ 1333.08 yd3
B = bh
= 8(8)
= 64
V = 1/3 Bh
= 1/3 (64)
= 21.33 ft3
(10)
8
B = 1/2bh
= 1/2(6)(8)
= 24
V = 1/3 Bh
= 1/3 (24)
= 120 ft3
(15)
4
3
B = bh
= 8(6)
= 48
V = 1/3 Bh
= 1/3 (48)
= 48 yd3
(3)
5
1010
B = bh
= 10(10)
= 100
V = 1/3 Bh
= 1/3 (100)
= 400 cm3
(12)
V = 1/3 πr2h
96π =1/3 πr2(8) π π96 = 1/3 r2(8) (3) (3)
288 = r2(8) 8 8
36 = r2
6 = r
V = 1/3 πr2h
2500π =1/3 π 52(h) π π2500 = 1/3 (25)(h) (3) (3)
7500 = 25h 25 25
300 = h
11-4 worksheet
ASSIGNMENT
LESSON 11-5
I can find surface area of spheres
I can find volume of spheres
V =4πr3
3
SA = 4πr2
V =2πr3
3
SA = 4πr2
= 4π(6)2
= 144π cm2
≈ 452.39 cm2
V =4πr3
3
=4π(6)3
3
= 288π cm3
≈ 904.78 cm3
SA = 4π(4)2
= 64π cm2 ≈ 201.06 cm2
V =4π(4)3
3
= 85.3π cm3
≈ 268.08 cm3
V =2πr3
3
=2π(16)3
3
= 2730.7π m3
≈ 8578.64 m3
V =2π(10)3
3
= 666.6π in3
≈ 2094.44 in 3
C = πd58 = πd
18.46 = d9.23 = r
SA = 4π(9.23)2
≈ 1070.57 m2
9.23 = r
V =4π(9.23)3
3
≈ 3293.77 cm3
V =4πr3
3
288π =4πr3
3
216 = r3
6 = r
SA = 4π(6)2
= 144π cm2
SA = 4πr2
324π = 4πr2
81 = r2
9 = r
V =4π(9)3
3
= 972π in3
11-5 worksheet
ASSIGNMENT
LESSON 11-6
I can find the volume of composite figures
cone + cylinder4
cone:V = 1/3 πr2h
= 1/3 π(3)24
= 12π
cylinder:V = πr2h
= π(3)25.1
= 45.9π
Total : 57.9π ≈ 181.9 cm3
rectangular prism
V = Bh
= 2100 (10)
= 21000
triangular prism
V = Bh
= 120 (70)
= 8400
Total = 29,400 ft3
11-6 worksheet
ASSIGNMENT
LESSON 11-7
I can identify properties of similar solids
I can find volume and surface area of similar solids
shapesize
a : b
a2 : b2
a3 : b3
congruent similar
1 : 3
similar
2 : 1
neither
1 : 2
12 : 22 or 1 : 4
13 : 23 or 1 : 8
8 : 5
82 : 52 or 64 : 25
83 : 53 or 512 :125
12 : 15
4
5
4 : 5
=10
x12.5 m
42 : 52 or 16 : 25 16
25=
280x 437.5 m2
43 : 53 or 64 :125 64
125=
400x 781.25 m3
8 : 6
4
3
4 : 3
=11
x8.25 cm
42 : 32 or 16 : 916
9=
x325 577.78 cm2
43 : 33 or 64 :27 64
27=
1345x 567.42 cm3
11-6 worksheet
ASSIGNMENT