Chapter 11: Surface Area & Volume 11.2 & 11.3 Surface Area of Prisms, Cylinders, Pyramids, & Cones

Definitions prism: bases: lateral faces: altitude: height: polyhedron with exactly two congruent, parallel faces bases: the parallel faces of a prism lateral faces: the nonparallel faces of a prism altitude: perpendicular segment that joins the planes of the bases height: length of an altitude

Prisms right prism oblique prism lateral faces are rectangles and a lateral edge is an altitude oblique prism slanted prism

Surface Area lateral area of a prism surface area of a prism sum of the areas of the lateral faces surface area of a prism sum of the lateral area and the area of the two bases

Example 1 Use a net to find the surface area of the prism:

Example 1a Use a net to find the surface area of the triangular prism:

Example 2 What is the surface area of the prism?

Example 2a Use formulas to find the lateral area and surface area of a hexagonal prism with side of length 6 m, and prism height of 12 m.

Theorem 11-1 The lateral area of a right prism is the product of the perimeter of the base and the height. LA = ph The surface area of a right prism is the sum of the lateral area and the areas of the two bases. SA = LA + 2B

Cylinders two congruent parallel bases that are circles altitude: perpendicular segment that joins the planes of the bases height: length of an altitude

Cylinders lateral area: surface area: turns out to be a rectangle sum of the lateral area and the areas of the two circular bases

Theorem 11-2 The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder. LA = 2πrh = πdh The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases. SA = LA + 2B = 2πrh + 2πr2

Example 3 The radius of the base of a cylinder is 4 in. and its height is 6 in. Find the surface area of the cylinder in terms of π.

Example 3a Find the surface area of a cylinder with height 10 cm and radius 10 cm in terms of π.

Definitions pyramid: regular pyramid: slant height: polyhedron in which one face (base) can be ANY polygon and the other faces (lateral faces) are triangles that meet at a common vertex regular pyramid: pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles slant height: length of the altitude of a lateral face of the pyramid

Pyramid lateral area sum of the areas of the congruent lateral faces

Theorem 11-3 The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height. LA = ½ p l The surface area of a regular pyramid is the sum of the lateral area and the area of the base. SA = LA + B

Example 1 Find the surface area of the hexagonal pyramid:

Example 1a Find the surface area of a square pyramid with base edges 5 m and slant height 3 m.

Cones base is a circle, “pointed” like a pyramid right cone: altitude is a perpendicular segment from the vertex to the center of the base height is the length of the altitude slant height: distance from the vertex to a point on the edge of the base

Theorem 11-4 The lateral area of a right cone is half the product of the circumference of the base and the slant height. LA = ½·πr·l = πrl The surface area of a right cone is the sum of the lateral area and the area of the base. SA = LA + B = πrl + πr2

Example 3 Find the surface area of the cone in terms of π, with a radius of 15 cm and slant height of 25 cm.

Example 4a Find the lateral area of a cone with radius 15 in and height 20 in.

Homework p. 611: 1-7, 8, 14 p. 620: 2-12 even, 18, 20