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
CHAPTER 12AREAS AND VOLUMES OF SOLIDS
12-3CYLINDERS AND CONES
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.
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.
CYLINDER
H
r
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
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)
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
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).
CONE
H
r
l
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
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
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
CLASSWORK/HOMEWORK
12-3 ASSIGNMENTClasswork:• Pg. 492 Classroom Exercises 2-8 evenHomework:• Pgs. 492-493 Written Exercises 2-18
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