Geometry 12.4 Volume of Prisms and Cylinders [email protected].
Unit 9: Solid Geometry I. Prisms · Unit 9: Solid Geometry Lesson 3: Surface Area of Prisms &...
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Unit 9: Solid Geometry Lesson 3: Surface Area of Prisms & Cylinders (12.2) Learning Targets: 9I Draw the net of a prism, and use it to develop a formula for the surface area of a right prism. 9K Derive the formula for the surface area of a right cylinder, and use the formula. 9J Find the surface area of a right prism. 9P Solve real world problems involving finding volume or surface area. 9S Find the surface area and volume of a sphere. Standards 8.0 & 9.0 I. Prisms lateral edges segments connecting the lateral faces lateral faces other faces bases two congruent faces I. Prisms Surface Area sum of ALL FACES think: "when wrapping a present, you wrap all sides" Right Hexagonal Prism lateral area Net Unfold your prism think: "peeling a banana" Example of a NET Prism Net Prism Unfold or Peel
Transcript of Unit 9: Solid Geometry I. Prisms · Unit 9: Solid Geometry Lesson 3: Surface Area of Prisms &...
Unit 9: Solid GeometryLesson 3: Surface Area of Prisms & Cylinders
(12.2)
Learning Targets:9I Draw the net of a prism, and use it to develop a formula for the surface area of a right prism.9K Derive the formula for the surface area of a right cylinder, and use the formula.9J Find the surface area of a right prism.9P Solve real world problems involving finding volume or surface area.9S Find the surface area and volume of a sphere.
Standards 8.0 & 9.0
I. Prisms
lateral edges segments connecting the lateral faces
lateral faces other faces
bases two congruent faces
I. Prisms
Surface Area sum of ALL FACES think: "when wrapping a present, you wrap all sides"
Right Hexagonal Prism
lateral area
Net Unfold your prismthink: "peeling a banana"
Example of a NET Prism
Net Prism
Unfold or Peel
Investigating Surface Area PrismGoal: Find the surface area using a net prism. (Think "wrapping a present").
Directions:1. Copy the net prism (p.727) on a piece of graph paper. Label the sections AF.
2. Cut out the net and fold it along the dotted lines to form a rectangular prism.
Investigate:
1. Find the Surface Area: The surface area of a prism is the sum of the area of its faces (base and lateral faces). Find the surface area of the polyhedron. (Each square on the graph paper measures 1 unit by 1 unit).
Section A B C D E F Total
Area
2. Lay the net flat again and find the following measures:
A: the area of rectangle A (base) =P: the perimeter of rectangle A (base) = h: the height of rectangles B, C, D, and E =
(note: height is perpendicular to the A)
3. Using the values from #2, find:
2A + Ph =
4. Compare #3 and #1 values. What do you notice?
Surface Area = _________
Surface Area = sum of Lateral Area + area of 2 bases
Surface Area = 2B + LA OR SA = 2B + php = perimeter of BASEh = height
Theorem 12.2 Surface Area of a Right Prism
LA
I. Prisms
B = area of base
I. Prisms
A
B C
D
E
F G
H
Example 1:
Surface Area = sum of Lateral Area + 2 basesSA = 2B + ph
p = perimeter of BASEh = height
B area of base
Step 1: Find the area of your base.
Step 2: Find the perimeter of your base.
Step 3: Find the height (perpendicular to the base).
Step 4: Plug into Surface Area formula.
AB C
D
E
F GH
Example 2I. Prisms
Step 1: Find the area of your base.
Step 2: Find the perimeter of your base and height (perpendicular to the base).
Step 3: Plug into Surface Area formula.
Let's Practice!
Worksheet 6.4 #811 all
I. Prisms
Example 3:
A
B
C
D
E
FA
B
C
Surface Area = sum of Lateral Area + 2 basesSA = 2B + ph
p = perimeter of BASEh = height
B area of base
Step 1: Find the area of your base.
Step 2: Find the perimeter of your base and height (perpendicular to the base).
Step 3: Plug into Surface Area formula.
A
B
C
D
E
F
I. Prisms
Example 4:
Surface Area = sum of Lateral Area + 2 basesSA = 2B + ph
p = perimeter of BASEh = height
B area of base
Step 1: Find the area of your base.
Step 2: Find the perimeter of your base and height (perpendicular to the base).
Step 3: Plug into Surface Area formula.
4 ft.
3 ft.
2 ft.
AB
C
D
EF
I. PrismsSurface Area = sum of Lateral Area + 2 bases
SA = 2B + php = perimeter of BASEh = height
B area of base
Example 5:
F E
D
Step 1: Find the area of your base.
Step 2: Find the perimeter of your base and height (perpendicular to the base).
Step 3: Plug into Surface Area formula.
Let's Practice!
Triangular Prism Worksheet #14
base areas
(circles)
lateral area area of the curved surface
II. Cylinder
Right Cylinder segment joining centers of the bases is
Take apart a cylinder:
Lateral Area =circumference x height
LA = 2πrh
Area of Bases = 2πr2
Surface Area = sum of 2 bases + lateral area
SA = 2πr2 + 2πrh
Net of a Cylinder
II. Cylinder
a)Example 1:
b) Find the lateral area of the cylinder.
Surface Area = sum of 2 bases + lateral area
SA = 2πr2 + 2πrh
II. Cylinder
a)
b) Find the lateral area of the cylinder.
Example 2:
II. CylinderExample 3: Find the surface area of a right cylinder that has a diameter of 10 in. and a height of 10 in.
II. Cylinder
Example 4:Find the height of the cylinder. The radius is 4 cm and the surface area is 160 cm2.
4
Surface Area = sum of 2 bases + lateral area
SA = 2πr2 + 2πrh
Let's Practice!
Worksheet 12.2 Practice B #18, 1214, 17
