chapter 12 areas and volumes of solids 12-3 cylinders and cones

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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