lesson 8.6 surface areas of prisms and cylinders pp. 341-347
DESCRIPTION
Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347. Objectives: 1.To differentiate between surface area and lateral surface area of prisms and cylinders. 2.To derive and apply formulas for calculating the surface area of prisms and cylinders. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/1.jpg)
Lesson 8.6Surface Areas of Prisms
and Cylinderspp. 341-347
Lesson 8.6Surface Areas of Prisms
and Cylinderspp. 341-347
![Page 2: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/2.jpg)
Objectives:1. To differentiate between surface
area and lateral surface area of prisms and cylinders.
2. To derive and apply formulas for calculating the surface area of prisms and cylinders.
Objectives:1. To differentiate between surface
area and lateral surface area of prisms and cylinders.
2. To derive and apply formulas for calculating the surface area of prisms and cylinders.
![Page 3: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/3.jpg)
Remember that cylinders and cones with polygonal bases
are called prisms and pyramids, respectively.
Remember that cylinders and cones with polygonal bases
are called prisms and pyramids, respectively.
![Page 4: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/4.jpg)
Theorem 8.14
The surface area of a prism is the sum of the lateral surface area and the area of the bases: S = L + 2B.
The lateral surface area of a right prism is the product of its height and the perimeter of its base: L = pH.
Theorem 8.14
The surface area of a prism is the sum of the lateral surface area and the area of the bases: S = L + 2B.
The lateral surface area of a right prism is the product of its height and the perimeter of its base: L = pH.
![Page 5: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/5.jpg)
Find the lateral and total surface area of the following solid figure. Find the lateral and total surface area of the following solid figure.
8 in.8 in.
4 in.4 in.
12 in.12 in.
![Page 6: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/6.jpg)
8 in8 in 8 in8 in4 in4 in 4 in4 in
12 in12 in
8 in8 in
8 in8 in
4 in4 in
4 in4 in
24 in24 in
![Page 7: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/7.jpg)
Theorem 8.15
The surface area of a cylinder is the sum of the lateral surface area and the area of the bases: S = L + 2B.
The lateral surface area of a right cylinder is the product of its circumference and height: L = cH.
Theorem 8.15
The surface area of a cylinder is the sum of the lateral surface area and the area of the bases: S = L + 2B.
The lateral surface area of a right cylinder is the product of its circumference and height: L = cH.
![Page 8: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/8.jpg)
EXAMPLE Find the surface area for the circular cylinder. EXAMPLE Find the surface area for the circular cylinder.
66
99
S = L + 2B
S = cH + 2B
S = 2rH + 2r2
S = 2(6)(9) + 2(36)S = 108 + 72S = 180 ≈ 565 square units
S = L + 2B
S = cH + 2B
S = 2rH + 2r2
S = 2(6)(9) + 2(36)S = 108 + 72S = 180 ≈ 565 square units
![Page 9: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/9.jpg)
Find the lateral and total surface area of the following solid figure. Find the lateral and total surface area of the following solid figure.
8 in8 in
12 in12 in
![Page 10: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/10.jpg)
Find the lateral and total surface area of the following solid figure. Find the lateral and total surface area of the following solid figure.
88
88
12121616
![Page 11: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/11.jpg)
Homeworkpp. 345-347Homeworkpp. 345-347
![Page 12: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/12.jpg)
►A. Exercises1. Find the lateral surface area of the
right prism if the base is a square.
►A. Exercises1. Find the lateral surface area of the
right prism if the base is a square.
1212
2525
L = pHL = 4(12)(25)L = 1200 units2
L = pHL = 4(12)(25)L = 1200 units2
![Page 13: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/13.jpg)
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
3.
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
3.
553.53.5
88
L = pHL = 5(5)(8)L = 200 units2
L = pHL = 5(5)(8)L = 200 units2
B = ½apB = ½(3.5)(25)B = 43.75 units2
B = ½apB = ½(3.5)(25)B = 43.75 units2
![Page 14: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/14.jpg)
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
3.
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
3.
553.53.5
88
S = L + 2BS = 200 + 2(43.75)S = 287.5 units2
S = L + 2BS = 200 + 2(43.75)S = 287.5 units2
![Page 15: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/15.jpg)
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
5.
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
5.
88
2323
L = pHL = 6(8)(23)L = 1104 units2
L = pHL = 6(8)(23)L = 1104 units2
B = ½apB = ½apB = ½(4 3)(48)B = ½(4 3)(48)B = 96 3 units2B = 96 3 units2
![Page 16: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/16.jpg)
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
5.
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
5. S = L + 2B
88
2323
S = 1104 + 2(96 3)S = 1104 + 2(96 3)S = 1104 + 192 3S = 1104 + 192 3S ≈ 1436.6 units2S ≈ 1436.6 units2
![Page 17: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/17.jpg)
L = pHL = (106)(34)L = 3604 units2
L = pHL = (106)(34)L = 3604 units2
B = ½h(b1+b2)B = ½(9)(18+38)B = 252 units2
B = ½h(b1+b2)B = ½(9)(18+38)B = 252 units2
3821
34
1829
9
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
7.
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
7.
![Page 18: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/18.jpg)
3821
34
1829
9
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
7.
►A. ExercisesFind the lateral surface area and total surface area of the following figure.
7. S = L + 2BS = 3604 + 2(252)S = 3604 + 504 S = 4108 units2
S = L + 2BS = 3604 + 2(252)S = 3604 + 504 S = 4108 units2
![Page 19: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/19.jpg)
►B. Exercises13. The surface area of a cube is 1350 sq.
inches. Find the dimensions of this cube.
►B. Exercises13. The surface area of a cube is 1350 sq.
inches. Find the dimensions of this cube.
L = pHL = 4s(s)L = 4s2
L = pHL = 4s(s)L = 4s2
B = s2B = s2
S = L + 2BS = 4s2 + 2(s2)S = 6s2
1350 = 6s2
s2 = 225s = 15 inches
S = L + 2BS = 4s2 + 2(s2)S = 6s2
1350 = 6s2
s2 = 225s = 15 inches
![Page 20: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/20.jpg)
►B. Exercises15. Find the lateral area of a right circular
cylinder whose diameter is 10 3 feet and whose height is 27 feet.
►B. Exercises15. Find the lateral area of a right circular
cylinder whose diameter is 10 3 feet and whose height is 27 feet.
10 3
27 L = 270 3L = 270 3
L = 10 3 (27)L = 10 3 (27)
L = cHL = cH
L ≈ 1469.2 feet2L ≈ 1469.2 feet2
![Page 21: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/21.jpg)
►C. Exercises20. Find the surface area of the napkin
ring.
►C. Exercises20. Find the surface area of the napkin
ring.
diam.4 cmdiam.4 cm
3 cm3 cm0.4 cm0.4 cm
![Page 22: Lesson 8.6 Surface Areas of Prisms and Cylinders pp. 341-347](https://reader030.vdocuments.mx/reader030/viewer/2022032607/568130e5550346895d96fbe8/html5/thumbnails/22.jpg)
■ Cumulative ReviewDefine each term.■ Cumulative ReviewDefine each term.
24. circle25. tangent26. supplementary angles27. congruent angles28. circumcenter
24. circle25. tangent26. supplementary angles27. congruent angles28. circumcenter