Surface area of prisms, cylinders, cones, and pyramids

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Presentation transcript:

Surface area of prisms, cylinders, cones, and pyramids Chapter 12.2 and 12.3 Surface area of prisms, cylinders, cones, and pyramids

Lateral Area Faces that are not bases are called lateral faces. Lateral faces intersect at lateral edges. The lateral area (L) of a prism is the sum of the area of the lateral faces.

Example 1 Find the lateral area of the regular hexagonal prism. Lateral Area of a Prism Example 1 Find the lateral area of the regular hexagonal prism.

Example 1 Find the lateral area of the regular octagonal prism. A. 162 cm2 B. 216 cm2 C. 324 cm2 D. 432 cm2

Surface Area Surface area of a prism is the sum of the lateral area and the areas of the bases.

Example 2 Find the surface area of the rectangular prism. Surface Area of a Prism Example 2 Find the surface area of the rectangular prism.

Example 2 Find the surface area of the triangular prism. A. 320 units2 B. 512 units2 C. 368 units2 D. 416 units2

Lateral Area and Surface Area of a Cylinder Example 3 Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

Example 3 Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. A. lateral area ≈ 1508 ft2 and surface area ≈ 2412.7 ft2 B. lateral area ≈ 1508 ft2 and surface area ≈ 1206.4 ft2 C. lateral area ≈ 754 ft2 and surface area ≈ 2412.7 ft2 D. lateral area ≈ 754 ft2 and surface area ≈ 1206.4.7 ft2

Find Missing Dimensions Example 4 MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can?

Example 4 Find the diameter of a base of a cylinder if the surface area is 480 square inches and the height is 8 inches. A. 12 inches B. 16 inches C. 18 inches D. 24 inches

Example 1 Find the lateral area of the square pyramid. Lateral Area of a Regular Pyramid Example 1 Find the lateral area of the square pyramid. Answer: The lateral area is 25 square centimeters.

Example 1 Find the lateral area of the square pyramid. A. 54 in2 B. 64 in2 C. 108 in2 D. 132 in2

Surface Area of a Square Pyramid Example 2 Find the surface area of the square pyramid to the nearest tenth.

Example 2 Find the surface area of the square pyramid to the nearest tenth. A. 96 in2 B. 124.3 in2 C. 138.5 in2 D. 156 in2

Surface Area of a Regular Pyramid Example 3 Find the surface area of the regular pyramid. Round to the nearest tenth.

Example 3 Find the surface area of the regular pyramid. Round to the nearest tenth. A. 198 in2 B. 228.5 in2 C. 255.5 in2 D. 316.3 in2

Concept

Lateral Area of a Cone Example 4 ICE CREAM A sugar cone has an altitude of 8 inches and a diameter of inches. Find the lateral area of the sugar cone.

Example 4 HATS A conical birthday hat has an altitude of 6 inches and a diameter of 4 inches. Find the lateral area of the birthday hat. A. 39.7 in.2 B. 43.6 in.2 C. 48.2 in.2 D. 53.1 in.2

Example 5 Find the surface area of the cone. Round to the nearest tenth. A. 58.2 cm2 B. 61.3 cm2 C. 63.6 cm2 D. 70.7 cm2