Presentation on theme: "Surface Area of Prisms and Cylinders"— Presentation transcript:
1 Surface Area of Prisms and Cylinders Warm UpLesson PresentationLesson Quiz
2 Warm-Up1. Evaluate 2xy + 2yz + 2xz for x = 9, y = 6, and z = 4.ANSWER2282. Evaluate 2πx2 + 2πxy for x = 4 and y = 7. Use 3.14 for π .ANSWER276.32
3 Warm-Up3. Find the area of a circle with radius 8 cm. Use 3.14 for π.ANSWERcm24. Find the area of a right triangle with hypotenuse 13 in. and a side length of 5 in.ANSWER30 in.2
4 Warm-Up5. Find the area of a regular pentagon with apothem 4.13 ft and side length 6 ft.ANSWER61.95 ft2
5 Example 1Find the surface area of a rectangular prism with height 2 centimeters, length 5 centimeters, and width 6 centimeters.SOLUTIONSTEP 1Sketch the prism. Imagine unfolding it tomake a net.
6 Example 1STEP 2Find the areas of the rectangles that form the faces of the prism.STEP 3Add the areas of all the faces to find thesurface area.The surface area of the prism isS = 2(12) + 2(10) + 2(30)= 104 cm2.
7 Example 2Find the surface area and lateral area of the right pentagonal prism.SOLUTIONSTEP 1Find the area of a pentagonal base. Use the formula of a regular polygon from page 793.Apothem a = √ 62 –3.5252≈ 4.86Perimeter P = 5(7.05)= 35.25Area of base B = aP= (0.5)(4.86)(35.25) 85.66
8 Example 2STEP 2Use the formula for the surface area of a right prism.S = 2B + Ph≈ 2(85.66) + (35.25)(9)≈The surface area of the right pentagonal prism is about square feet. The lateral area is Ph ≈ (35.25)(9) ≈ square feet.
9 Guided Practice1. Draw a net of a triangular prism.ANSWER
10 Guided Practice2. Find the surface area and lateral area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches using (a) a net and (b) the formula for the surface area of a right prism.ANSWERa. Left and right faces: 7 · 4 = 28 in.2Top and bottom faces: 3 · 4 = 12 in.2Front and back faces: 3 · 7 = 21 in.2S = 2(28) + 2(12) + 2(21) = 122 in.2Lateral area = 2(28) + 2(21) = 98 in.2b. S = 2B + Ph = 2(3 · 4 ) + 14 · 7 = 122 in.2Lateral area = Ph = 14 · 7 = 98 in.2
11 Example 3You are wrapping a stack of 20 compact discs using a shrink wrap. Each disc is cylindrical with height 1.2 millimeters and radius 60 millimeters. What is the minimum amount of shrink wrap needed to cover the stack of 20 discs?COMPACT DISCS
12 Example 3SOLUTIONThe 20 discs are stacked, so the height of the stack will be 20(1.2) = 24 mm. The radius is 60 millimeters. The minimum amount of shrink wrap needed will be equal to the surface area of the stack of discs.S = 2πr πrhSurface area of a cylinder.= 2π(60) π(60)(24)Substitute known values.≈ 31,667Use a calculator.You will need at least 31,667 square millimeters, or about 317 square centimeters of shrink wrap.
13 Example 4Find the height of the right cylinder shown, which has a surface area of square meters.SOLUTIONSubstitute known values in the formula for the surface area of a right cylinder and solve for the height h.S = 2πr2 + 2πrhSurface area of a cylinder.= 2π(2.5)2 + 2π(2.5)hSubstitute known values.= 12.5π + 5πhSimplify.– 12.5π = 5πhSubtract 12.5π from each side.≈ 5πhSimplify. Use a calculator.7.5 ≈ hDivide each side by 5π.
14 Guided Practice3. Find the surface area and lateral area of a right cylinder with height 18 centimeters and radius 10 centimeters. Round your answer to two decimal places.cm2; cm2ANSWER4. Find the radius of a right cylinder with height 5 feet and surface area 208π square feet.8 ftANSWER
15 Lesson Quiz1. Find the surface area of the solid formed by the net.ANSWER288 cm2
16 Lesson QuizFind the surface of the right prism or right cylinder.2.ANSWER2580 m2
17 Lesson QuizFind the surface of the right prism or right cylinder.3.ANSWERyd2
18 Lesson Quiz4. A rectangular prism has surface area 1848 ft2. Solve for x.ANSWER18