Surface Areas of Prisms and Cylinders LESSON 12–2

Lesson Menu 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

Over Lesson 12–1 5-Minute Check 1 Use isometric dot paper to sketch a cube 2 units on each edge. A.B. C.D.

Over Lesson 12–1 5-Minute Check 2 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.

Over Lesson 12–1 5-Minute Check 3 Use isometric dot paper and the orthographic drawing to sketch a solid. A.B. C.D.

Over Lesson 12–1 5-Minute Check 4 A.triangle B.rectangle C.trapezoid D.rhombus Describe the cross section of a rectangular solid sliced on the diagonal.

TEKS 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)

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

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

Concept

Example 1 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. Answer:The lateral area is 360 square centimeters. Lateral area of a prism P = 30, h = 12 Multiply.

Example 1 A.162 cm 2 B.216 cm 2 C.324 cm 2 D.432 cm 2 Find the lateral area of the regular octagonal prism.

Concept

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

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

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

Concept

Example 3 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  rhLateral area of a cylinder =2  (14)(18)Replace r with 14 and h with 18. ≈1583.4Use a calculator.

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

Example 3 A.lateral area ≈ 1508 ft 2 and surface area ≈ ft 2 B.lateral area ≈ 1508 ft 2 and surface area ≈ ft 2 C.lateral area ≈ 754 ft 2 and surface area ≈ ft 2 D.lateral area ≈ 754 ft 2 and surface area ≈ ft 2 Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

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

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

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

Surface Areas of Prisms and Cylinders LESSON 12–2