Slide 61 / 159 Volume of a Pyramid (Area of Base x Height) 3 The Volume of a 1 click to reveal (Area of Base x Height) Pyramid is 1/3 the 3 volume of a prism with the same base area ( B ) and height ( h ). Note: Pyramids are named by the shape of their base.
Slide 62 / 159 Volume Example: Find the volume of the pyramid shown below. 1 V = Bh 3 1 V = Bh 3 =5 m side length = 4 m
Slide 63 / 159 28 Find the Volume of a triangular pyramid with base edges of 8 in, base height of 6.9 in and a pyramid height of 10 in. 10 in 6.9 in 8 in
Slide 64 / 159 29 Find the volume. 15.3 cm 7 cm 8 cm
Slide 65 / 159 Surface Area Return to Table of Contents
Slide 66 / 159 Surface Area of Prisms Return to Table of Contents
Slide 67 / 159 Surface Area Surface Area is the sum of the areas of all outside surfaces of a 3-D figure. To find surface area, you must find the area of each surface of the figure then add them together. What type of figure is pictured? 6 in How many surfaces are there? 3 in How do you find the area of each 8 in surface?
Slide 68 / 159 Surface Area 6 in 3 in 8 in Bottom Top Left Right Front Back SUM 8 8 6 6 8 8 x 3 x 3 x 3 x 3 x 6 x 6 24 24 18 18 48 48 = 180 in 2 18 6 in 6 in 48 6 in +48 3 in 3 in 3 in 8 in 8 in 8 in 180 in 2
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Slide 71 / 159 Arrangement of Unit Cubes Surface Area Activity Click the link below for the activity Lab #2: Surface Area Activity
Slide 72 / 159 Teachers: Use this Mathematical Practice Pull Tab for the next 4 SMART Response slides.
Slide 73 / 159 30 Which arrangement of 27 cubes has the least surface area? A 1 x 1 x 27 B 3 x 3 x 3 C 9 x 3 x 1
Slide 74 / 159 31 Which arrangement of 12 cubes has the least surface area? A 2 x 2 x 3 B 4 x 3 x 1 C 2 x 6 x 1 D 1 x 1 x 12
Slide 75 / 159 32 Which arrangement of 25 cubes has the greatest surface area? A 1 x 1 x 25 B 1 x 5 x 5
Slide 76 / 159 33 Which arrangement of 48 cubes has the least surface area? A 4 x 12 x 1 B 2 x 2 x 12 C 1 x 1 x 48 D 3 x 8 x 2 E 4 x 2 x 6 F 4 x 3 x 4
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Slide 79 / 159 34 How many faces does the figure have? 6 m 2 m 4 m
Slide 80 / 159 35 How many area problems must you complete when finding the surface area? 6 m 2 m 4 m
Slide 81 / 159 36 What is the area of the top or bottom face? 6 m 2 m 4 m
Slide 82 / 159 37 What is the area of the left or right face? 6 m 2 m 4 m
Slide 83 / 159 38 What is the area of the front or back face? 6 m 2 m 4 m
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Slide 85 / 159 Find the Surface Area 1. Draw and label ALL faces; use the net, if it's helpful 2. Find the correct dimensions for each face 3. Calculate the AREA of EACH face 4. Find the SUM of ALL faces 5. Label Answer 5 yd go on to see steps 5 yd 4 yd 9 yd 6 yd
Slide 86 / 159 Surface Area 5 yd 5 yd 5 yd 5 yd 4 yd 4 yd 9 yd 9 yd 6 yd 6 yd Triangles Bottom Rectangle 4 9 CLICK TO REVEAL x 6 x 6 CLICK TO REVEAL 24 / 2 = 12 54 x 2 24 Total Left/Right Rectangles Surface (Same size since isosceles) Area 5 yd CLICK TO REVEAL 24 5 5 yd 54 x 9 4 yd CLICK TO REVEAL 9 yd + 90 45 6 yd 168 yd 2 x 2 90
Slide 87 / 159 Find the Surface Area Using the Net 5 yd 5 yd 4 yd 9 yd 6 yd Triangles 4 Middle Rectangle x 6 CLICK TO REVEAL 9 24 / 2 = 12 Total CLICK TO REVEAL x 6 x 2 Surface 54 24 Area CLICK TO REVEAL 24 Left/Right Rectangles 54 CLICK TO REVEAL (Same size since isosceles) + 90 5 x 9 = 45 x 2 = 90 168 yd 2
Slide 88 / 159 Find the Surface Area 1. Draw and label ALL faces; use the net if it's helpful 2. Find the correct dimensions for each face 3. Calculate the AREA of EACH face 4. Find the SUM of ALL faces 5. Label Answer 9 cm TRY THIS ONE 9 cm 7.8 cm 11 cm 9 cm
Slide 89 / 159 Surface Area 9 cm 9 cm 9 cm 9 cm 7.8 cm 11 cm 7.8 cm 11 cm 9 cm 9 cm Triangles Rectangles A = 9(11) = 99 cm 2 A = 7.8 x 9 2 A = 99 x 3 = 297 cm 2 A = 35.1 cm 2 x 2 70.2 cm 2
Slide 90 / 159 Surface Area 9 cm 9 cm 7.8 cm 11 cm 9 cm Triangles A = 7.8 x 9 2 Rectangles A = 35.1 cm 2 x 2 A = 9(11) = 99 cm 2 70.2 cm 2 click to reveal A = 99 x 3 = 297 cm 2 click to reveal
Slide 91 / 159 40 Find the surface area of the shape below. 1. Draw and label ALL faces; use the net if it's helpful 2. Find the correct dimensions for each face 3. Calculate the AREA of EACH face 4. Find the SUM of ALL faces 5. Label Answer 47 ft 50 ft 21 ft 42 ft
Slide 92 / 159 Find the Surface Area. 9 cm 3 cm 4 cm 15 cm 5 cm 6 cm
Slide 93 / 159 9 cm 3 cm 4 cm 15 cm 5 cm 6 cm Top Rectangle Side Rectangles Bottom Rectangle Trapezoids 12 5 6 12 x 15 x 15 x 15 + 6 180 75 90 18 x 2 x 4 click to reveal click to reveal 150 72 / 2 = 36 x 2 click to reveal 72 click to reveal
Slide 94 / 159 41 Find the surface area of the shape below. 8 cm 6 cm 9 cm 10 cm
Slide 95 / 159 42 Find the surface area of the shape below. 2 cm 10 cm 6 cm 6 c m 10 cm
Slide 96 / 159 Surface Area of Pyramids Return to Table of Contents
Slide 97 / 159 Surface Area of Pyramids What is a pyramid? Polyhedron with one base and triangular faces that meet at a vertex click to reveal How do you find Surface Area? Sum of the areas of all the surfaces of a 3-D Figure click to reveal
Slide 98 / 159 Find the Surface Area. 17.5 cm go on to see steps 7 cm 17.4 cm 8 cm
Slide 99 / 159 Find the Surface Area. Bottom Front/Back Left/Right Rectangle Triangles Triangles 8 A = 1 A = 1 2 bh(2) 2 bh(2) x 7 2 56 cm A = 1 A = 1 2 (8)(17.4)(2) 2 (7)(17.5)(2) A = 139.2 cm 2 A = 122.5 cm 2
Slide 100 / 159 Surface Area Find the surface area of a square pyramid with base edge of 4 inches and triangle height of 3 inches. 3 in Base 4 Triangles Surface Area 4 16 x 4 + 24 16 40 in 2 click to reveal click to reveal click to reveal 4 in
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