12.2 Surface Area of Prisms and Cylinders

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12.2 Surface Area of Prisms and Cylinders
GEOMETRY: Chapter 12 12.2 Surface Area of Prisms and Cylinders

A prism is a polyhedron with two congruent faces, called bases, that lie in parallel planes.
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The other faces, called lateral faces are parallelograms formed by connecting the corresponding vertices of the bases. The segments connecting these vertices are lateral edges. Prisms are classified by the shapes of their bases. Images taken from:

The surface area of a polyhedron is the sum of the areas of its faces
The surface area of a polyhedron is the sum of the areas of its faces. The lateral area of a polyhedron is the sum of the areas of its lateral faces.

Ex. 1 Find the surface area of a rectangular prism with height 3 cm, length 6 cm, and width 8 cm. Answer: 180cm2

Right prisms: The height of a prism is the perpendicular distance between its bases. In a right prism, each lateral edge is perpendicular to both bases. Images taken from: Geometry. McDougal Littell: Boston, P. 804.

A prism with lateral edges that are not perpendicular to the bases is an oblique prism.
Images taken from: Geometry. McDougal Littell: Boston, P. 804.

The surface area S of a right prism is S = 2B + Ph = aP + Ph,
Theorem 12.2: Surface Area of a Right Prism The surface area S of a right prism is S = 2B + Ph = aP + Ph, where a is the apothem of the base, B is the area of a base, P is the perimeter of a base and h is the height. Images taken from: Geometry. McDougal Littell: Boston, P. 731.

Ex. 2. :Find the surface area of the right hexagonal prism.
Answer: ft2 Images taken from: Geometry. McDougal Littell: Boston, P. 804.

A cylinder is a solid with congruent circular bases that lie in parallel planes. In a right cylinder, the segment joining the centers of the bases is perpendicular to the bases. Images taken from: Geometry. McDougal Littell: Boston, P. 805.

The surface area of a right cylinder is
Theorem 12.3: Surface Area of Right Cylinder The surface area of a right cylinder is 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. Images taken from: Geometry. McDougal Littell: Boston, P. 805.

Ex. 3 You are wrapping a poster in a cardboard cylinder. The cylinder has a height of 36in. And a radius of 4 in. What is the minimum amount of cardboard needed to cover the poster, including the two bases of the cylinder? Answer: at least in2 Images taken from: Geometry. McDougal Littell: Boston, P. 805.

Ex. 4 Find the height of the right cylinder, which has a surface area of cm2. Answer: 7.2cm Images taken from: Geometry. McDougal Littell: Boston, P. 806.

12.2, p. 731, #3-10 all, 13-15, all (19 questions)