11.2 Surface Areas of Prisms and Cylinders

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11.2 Surface Areas of Prisms and Cylinders A prism is a polyhedron with two congruent, parallel faces, called bases. The other faces are lateral faces. You name prisms based on using the shapes of the bases.

Prisms An altitude of a prism is a perpendicular segment that joins the planes of the bases. The height, h, of a prism is the length of an altitude. A prism may either be right or oblique. Right prism – the lateral faces are rectangles and a lateral edge is an altitude. Oblique prism – some or all of the lateral faces are nonrectangular.

Prisms Lateral Area (L.A.) of a prism is the sum of the areas of the lateral faces. Surface Area (S.A.) of a prism is the sum of the lateral area and the area of the two bases.

Find the Surface Area of a Prism What is the surface area of the prism?

Lateral and Surface Areas of a Prism The lateral area of a right prism is the product of the perimeter of the base and the height of the prism. L.A. = Ph The surface area of a right prism is the sum of the lateral area and the areas of the two bases. S.A. = L.A. + 2B

Using Formulas to Find Surface Area of a Prism What is the surface area of the prism?

Cylinders A cylinder is a solid that has two congruent parallel bases that are circles. An altitude of a cylinder is a perpendicular segment that joins the planes of the bases. The height, h, of a cylinder is the length of an altitude. In a right cylinder, the segment joining the centers of the bases is an altitude. In an oblique cylinder, the segment joining the centers is not perpendicular to the planes containing the bases.

Lateral and Surface Areas of a Cylinder The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder. L.A. = 2πrh or L.A. = πdh The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases. S.A. = L.A. + 2B or S.A. = 2πrh + 2πr²

Finding Surface Area of a Cylinder The radius of the base of a cylinder is 4 in. and its height is 6 in. What is the surface area of the cylinder in terms of π?

Finding Lateral Area of a Cylinder You are using a cylindrical stencil roller to paint patterns on your floor. What area does the roller cover in one full turn if it has a diameter of 2.5 in. and a height of 6 in.?

More Practice!!!!! Homework – Textbook p. 703 – 704 #1 – 20 ALL.