CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-3 CYLINDERS 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 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.

CYLINDER H r

THEOREM 12-5 The 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 The volume of a cylinder equals the area of a base times the height of the cylinder. V = r² H

CONE A 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 12-7 The 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 AREA Much 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 12-8 The 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 ASSIGNMENT Classwork: Pg. 492 Classroom Exercises 2-8 even Homework: Pgs Written Exercises 2-18 even