10 4 Surface Area of Prisms and Cylinders

10 -4 Surface Area of Prisms and Cylinders Preview Warm Up California Standards Lesson Presentation Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Warm Up 1. A triangular pyramid has a base area of 1. 2 m 2 and a height of 7. 5 m. What is the volume of the pyramid? 3 m 3 2. A cone has a radius of 4 cm and a height of 10 cm. What is the volume of the cone to the nearest cubic centimeter? Use 3. 14 for . 167 cm 3 Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders California Standards MG 2. 1 Use formulas routinely for finding the perimeter and area of basic twodimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG 2. 2, MG 2. 3 Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Vocabulary surface area lateral face lateral area lateral surface Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders The surface area of a three-dimensional figure is the sum of the areas of all its surfaces. You can use centimeter cubes to explore the surface area of prisms. Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Additional Example 1 A: Finding Surface Area of Figures Built of Cubes Find the surface area of each figure. The figure is made up of congruent cubes. Draw each view of the figure. top front left 1 cm Find the area of each view. 12 + 8 + 6 + 12 + 8 + 6 = 52 bottom The surface area is 52 cm 2. Holt CA Course 1 back right

10 -4 Surface Area of Prisms and Cylinders Additional Example 1 B: Finding Surface Area of Figures Built of Cubes Find the surface area of each figure. The figure is made up of congruent cubes. Draw each view of the figure. top front left 1 cm Find the area of each view. bottom 8+8+6+8+8 + 6 = 44 The surface area is 44 cm 2. Holt CA Course 1 back right

10 -4 Surface Area of Prisms and Cylinders Check It Out! Example 1 A Find the surface area of each figure. The figure is made up of congruent cubes. Draw each view of the figure. top front left 1 cm Find the area of each view. bottom 8+8+4+8+8 + 4 = 40 The surface area is 40 cm 2. Holt CA Course 1 back right

10 -4 Surface Area of Prisms and Cylinders Check It Out! Example 1 B Find the surface area of each figure. The figure is made up of congruent cubes. Draw each view of the figure. top front left 1 cm Find the area of each view. bottom 8+9+6+8+9 + 6 = 46 The surface area is 46 cm 2. Holt CA Course 1 back right

10 -4 Surface Area of Prisms and Cylinders The lateral faces of a prism are parallelograms that connect the bases. The lateral area of a prism is the sum of the areas of the lateral faces. Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Additional Example 2: Finding Surface Area of Prisms Find the surface area of the figure to the nearest tenth. The figure is a triangular prism. S = 2 B + Ph = 2( 1 • 8 • 3) + (18)(10) 2 = 204 ft 2 Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Check It Out! Example 2 Find the surface area of the figure to the nearest tenth. The figure is a triangular prism. S = 2 B + Ph = 2( 1 • 7 • 6) + (21)(10) 2 = 252 cm 2 Holt CA Course 1 7 cm 10 cm 7 cm 6 cm 7 cm

10 -4 Surface Area of Prisms and Cylinders The lateral surface of a cylinder is the curved surface. Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Additional Example 3: Finding Surface Area of Cylinders Find the surface area of the cylinder to the nearest tenth. Use 3. 14 for p. S = 2 r 2 + 2 rh = 2 (42) + 2 (4)(6) = 80 in 2 251. 2 in 2 Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Check It Out! Example 3 Find the surface area of the cylinder to the nearest tenth. Use 3. 14 for p. 15 cm S = 2 r 2 + 2 rh = 2 (152) + 2 (15)(3) = 540 in 2 1695. 6 cm 2 Holt CA Course 1 3 cm

10 -4 Surface Area of Prisms and Cylinders Additional Example 4: Application A cylindrical soup can is 7. 6 cm in diameter and 11. 2 cm tall. Estimate the area of the label that covers the side of the can. The cylinder’s diameter is about 8 cm, and its height is about 11 cm. L = 2 rh = 2 (4)(11) Only the lateral surface needs to be covered. Diameter ≈ 8 cm, so r ≈ 4 cm. = 88 ≈ 267. 3 cm 2 Holt CA Course 1

10 -4 Surface Area of Prisms and Cylinders Check It Out! Example 4 A cylindrical storage tank that is 6 ft in diameter and 12 ft tall needs to be painted. Estimate the area to be painted. S = 2 r 2 + 2 rh = 2 (32) + 2 (3)(12) = 90 ft 2 282. 6 ft 2 Holt CA Course 1 The diameter is 6 ft, so r = 3 ft.

10 -4 Surface Area of Prisms and Cylinders Lesson Quiz Find the surface area of each figure to the nearest tenth. Use 3. 14 for p. 1. the triangular prism 360 cm 2 2. the cylinder 320. 3 in 2 3. All outer surfaces of a box are covered with gold foil, except the bottom. The box measures 6 in. long, 4 in. wide, and 3 in. high. How much gold foil was used? 84 in 2 Holt CA Course 1