Surface Areas of Prisms and Cylinders LESSON 12–2 Surface Areas of Prisms and Cylinders

Five-Minute Check (over Lesson 12–1) TEKS Then/Now New Vocabulary Key Concept: Lateral Area of a Prism Example 1: Lateral Area of a Prism Key Concept: Surface Area of a Prism Example 2: Surface Area of a Prism Key Concept: Areas of a Cylinder Example 3: Lateral Area and Surface Area of a Cylinder Example 4: Real-World Example: Find Missing Dimensions Lesson Menu

Use isometric dot paper to sketch a cube 2 units on each edge. A. B. C. D. 5-Minute Check 1

Use isometric dot paper to sketch a triangular prism 3 units high with two sides of the base that are 5 units long and 2 units long. A. B. C. D. 5-Minute Check 2

Use isometric dot paper and the orthographic drawing to sketch a solid. A. B. C. D. 5-Minute Check 3

Describe the cross section of a rectangular solid sliced on the diagonal. A. triangle B. rectangle C. trapezoid D. rhombus 5-Minute Check 4

Mathematical Processes G.1(A), G.1(E) Targeted TEKS G.11(C) Apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. Mathematical Processes G.1(A), G.1(E) TEKS

You found areas of polygons. Find lateral areas and surface areas of prisms. Find lateral areas and surface areas of cylinders. Then/Now

lateral face lateral edge base edge altitude height lateral area axis composite solid Vocabulary

Concept

Find the lateral area of the regular hexagonal prism. Lateral Area of a Prism Find the lateral area of the regular hexagonal prism. The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters. Lateral area of a prism P = 30, h = 12 Multiply. Answer: The lateral area is 360 square centimeters. Example 1

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

Concept

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

Answer: The surface area is 360 square centimeters. Surface Area of a Prism Surface area of a prism L = Ph Substitution Simplify. Answer: The surface area is 360 square centimeters. Example 2

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

Concept

L = 2rh Lateral area of a cylinder Lateral Area and Surface Area of a Cylinder Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. L = 2rh Lateral area of a cylinder = 2(14)(18) Replace r with 14 and h with 18. ≈ 1583.4 Use a calculator. Example 3

S = 2rh + 2r2 Surface area of a cylinder Lateral Area and Surface Area of a Cylinder S = 2rh + 2r2 Surface area of a cylinder ≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4 and r with 14. ≈ 2814.9 Use a calculator. Answer: The lateral area is about 1583.4 square feet and the surface area is about 2814.9 square feet. Example 3

A. lateral area ≈ 1508 ft2 and surface area ≈ 2412.7 ft2 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 Example 3

L = 2rh Lateral area of a cylinder Find Missing Dimensions MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can? L = 2rh Lateral area of a cylinder 125.6 = 2r(8) Replace L with 15.7 ● 8 and h with 8. 125.6 = 16r Simplify. 2.5 ≈ r Divide each side by 16. Example 4

Answer: The radius of the soup can is about 2.5 inches. Find Missing Dimensions Answer: The radius of the soup can is about 2.5 inches. 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 4

Surface Areas of Prisms and Cylinders LESSON 12–2 Surface Areas of Prisms and Cylinders