Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.
-
Upload
amanda-barrett -
Category
Documents
-
view
305 -
download
1
Transcript of Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.
![Page 1: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/1.jpg)
Chapter 11: Surface Area & Volume
11.2 & 11.3
Surface Area of Prisms, Cylinders, Pyramids, & Cones
![Page 2: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/2.jpg)
Definitions• prism:
– polyhedron with exactly two congruent, parallel faces
• bases:– the parallel faces of a prism
• lateral faces:– the nonparallel faces of a prism
• altitude:– perpendicular segment that joins the planes of the
bases
• height:– length of an altitude
![Page 3: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/3.jpg)
Prisms• right prism
– lateral faces are rectangles and a lateral edge is an altitude
• oblique prism– slanted prism
![Page 4: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/4.jpg)
Surface Area
• lateral area of a prism– sum of the areas of the lateral faces
• surface area of a prism– sum of the lateral area and the area of the two
bases
![Page 5: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/5.jpg)
Example 1
• Use a net to find the surface area of the prism:
33
3
44
4
4
3
5
![Page 6: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/6.jpg)
Example 1a
• Use a net to find the surface area of the triangular prism:
12 cm6 cm
5 cm5 cm
![Page 7: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/7.jpg)
Example 2
• What is the surface area of the prism?
6 cm
4 cm3 cm
![Page 8: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/8.jpg)
Example 2a
• Use formulas to find the lateral area and surface area of a hexagonal prism with side of length 6 m, and prism height of 12 m.
![Page 9: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/9.jpg)
Theorem 11-1
• The lateral area of a right prism is the product of the perimeter of the base and the height.
LA = ph
• The surface area of a right prism is the sum of the lateral area and the areas of the two bases.
SA = LA + 2B
![Page 10: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/10.jpg)
Cylinders
• two congruent parallel bases that are circles
• altitude:– perpendicular segment that joins the planes of the
bases
• height:– length of an altitude
![Page 11: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/11.jpg)
Cylinders
• lateral area:– turns out to be a rectangle
• surface area:– sum of the lateral area and the areas of the two
circular bases
![Page 12: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/12.jpg)
Theorem 11-2
• The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder.
LA = 2πrh = πdh
• The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases.
SA = LA + 2B = 2πrh + 2πr2
![Page 13: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/13.jpg)
Example 3• The radius of the base of a cylinder is 4 in. and
its height is 6 in. Find the surface area of the cylinder in terms of π.
![Page 14: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/14.jpg)
Example 3a• Find the surface area of a cylinder with height
10 cm and radius 10 cm in terms of π.
![Page 15: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/15.jpg)
Definitions
• pyramid:– polyhedron in which one face (base) can be ANY
polygon and the other faces (lateral faces) are triangles that meet at a common vertex
• regular pyramid:– pyramid whose base is a regular polygon and
whose lateral faces are congruent isosceles triangles
• slant height:– length of the altitude of a lateral face of the pyramid
![Page 16: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/16.jpg)
Pyramid
• lateral area– sum of the areas of the congruent lateral faces
![Page 17: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/17.jpg)
Theorem 11-3
• The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height.
LA = ½ p l
• The surface area of a regular pyramid is the sum of the lateral area and the area of the base.
SA = LA + B
![Page 18: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/18.jpg)
Example 1• Find the surface area of the hexagonal
pyramid:
6 in
3 3 in
9 in
![Page 19: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/19.jpg)
Example 1a
• Find the surface area of a square pyramid with base edges 5 m and slant height 3 m.
![Page 20: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/20.jpg)
Cones
• base is a circle, “pointed” like a pyramid
• right cone:– altitude is a perpendicular segment from the vertex
to the center of the base– height is the length of the altitude
• slant height:– distance from the vertex to a point on the edge of
the base
![Page 21: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/21.jpg)
Theorem 11-4
• The lateral area of a right cone is half the product of the circumference of the base and the slant height.
LA = ½·πr·l = πrl
• The surface area of a right cone is the sum of the lateral area and the area of the base.
SA = LA + B = πrl + πr2
![Page 22: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/22.jpg)
Example 3• Find the surface area of the cone in terms of π,
with a radius of 15 cm and slant height of 25 cm.
![Page 23: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/23.jpg)
Example 4a
• Find the lateral area of a cone with radius 15 in and height 20 in.
![Page 24: Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones.](https://reader033.fdocuments.net/reader033/viewer/2022061411/56649ec75503460f94bd4348/html5/thumbnails/24.jpg)
Homework
• p. 611: 1-7, 8, 14
• p. 620: 2-12 even, 18, 20