Section 12.2 Surface Area of Prisms and Cylinders June 11, 2016.

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Presentation transcript:

Section 12.2 Surface Area of Prisms and Cylinders June 11, 2016

Goal 1 Finding the surface area of a prism.

Definitions (picture to follow)  prism: a polyhedron with two congruent faces, called bases, that are parallel to each other  lateral faces: (the sides) parallelograms formed by connecting corresponding verticies of the bases  height (altitude): the perpendicular distance between the bases of a prism

Right Rectangular Prism Base(2) lateral edges lateral faces height

More Definitions  right prism: each lateral edge is perpendicular to both bases, otherwise it is an oblique prism  slant height: the length of the oblique lateral edges  surface area: the sum of the areas of its faces(the area of the sides and bases)  lateral area: the sum of the areas of its lateral faces

Oblique Prism base(2) height slant height

Surface Area of a Right Prism Theorem 12.2 The surface area S of a right prism can be found using the formula S=2B+Ph, where B is the area of the base, P is the perimeter of the base, and h is the height.

Example 1 Find the surface area. 8 in. 5 in. 12 in.

Example 2 Find the surface area of the right prism. 6 in. 5 in. 10 in. 7 in. 5 in.

Goal 2 Finding the surface area of a cylinder.

Definitions  cylinder: a solid with parallel congruent circular bases  altitude: the perpendicular distance between its bases  lateral area: area of the curved surface (the sides)  surface area: the sum of the lateral area and the areas of the two bases

Right Cylinder base(2) height radius

Surface Area of a Right Cylinder Theorem 12.3 The surface area S of a right cylinder is S=2B+Ch=2πr 2 +2πrh, where B is the area of the base, C is the circumference of the base, r is the radius of the base and h is the height. Where, exactly, did this formula come from? If you can answer that, you will never forget it.

Example 3 Find the surface area. 4 ft. 3 ft.

Example 4 Find the height of the cylinder, given the surface area is sq. cm. 6.5 cm h

Homework p ,13-19, even, 48, 50-55