chapter 12 areas and volumes of solids 12-3 cylinders and cones
DESCRIPTION
CYLINDER VOCABULARY The specific pieces of a cylinder that we use to calculate measures include: 1.Altitude (height, H). The altitude joins the centers of both bases. 2.Radius (r). The radius of a base is also known as the radius of the cylinder.TRANSCRIPT
![Page 1: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/1.jpg)
CHAPTER 12AREAS AND VOLUMES OF SOLIDS
12-3CYLINDERS AND CONES
![Page 2: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/2.jpg)
CYLINDER
A cylinder is very similar to a prism in that it has two congruent bases.
The significant difference between a cylinder and a prism is that cylinders have circles for bases instead of polygons.
![Page 3: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/3.jpg)
CYLINDER VOCABULARYThe specific pieces of a cylinder that we
use to calculate measures include:
1. Altitude (height, H). The altitude joins the centers of both bases.
2. Radius (r). The radius of a base is also known as the radius of the cylinder.
![Page 4: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/4.jpg)
CYLINDER
H
r
![Page 5: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/5.jpg)
THEOREM 12-5
THEOREM 12-5The lateral area of a cylinder equals the
circumference of a base times the height of the cylinder.
L.A. = 2 r H
![Page 6: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/6.jpg)
TOTAL AREA
The total area of a cylinder is found by adding its lateral area with the areas of both of its bases.
T.A. = L.A. + 2( r²)
![Page 7: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/7.jpg)
THEOREM 12-6
THEOREM 12-6The volume of a cylinder equals the area of
a base times the height of the cylinder.
V = r² H
![Page 8: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/8.jpg)
CONEA cone is very similar to a pyramid
except for that it has a circle for a base instead of a polygon.
Just like a pyramid, a cone has an altitude (height, H) as well as a slant height (l).
![Page 9: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/9.jpg)
CONE
H
r
l
![Page 10: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/10.jpg)
THEOREM 12-7THEOREM 12-7The lateral area of a cone equals half of the
circumference of the base times the slant height.
L.A. = ½ (2 r l), or= r l
![Page 11: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/11.jpg)
TOTAL AREAMuch like the total area of a pyramid, the
total area of a cone can be found by adding its lateral area to the area of its base.
T.A. = L.A. + r²
![Page 12: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/12.jpg)
THEOREM 12-8THEOREM 12-8The volume of a cone equals one third the area
of the base times the height of the cone.
V = 1/3 ( r²) H
![Page 13: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS AND CONES](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b647f8b9ab0599aec19/html5/thumbnails/13.jpg)
CLASSWORK/HOMEWORK
12-3 ASSIGNMENTClasswork:• Pg. 492 Classroom Exercises 2-8 evenHomework:• Pgs. 492-493 Written Exercises 2-18
even