Preview Warm Up California Standards Lesson Presentation

Warm Up 1. A triangular pyramid has a base area of 1.2 m2 and a height of 7.5 m. What is the volume of the pyramid? 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 p. 3 m3 167 cm3

MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG2.2, MG2.3 California Standards

Vocabulary surface area lateral face lateral area lateral surface

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.

Additional Example 1A: 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 1 cm Find the area of each view. bottom back right 12 + 8 + 6 + 12 + 8 + 6 = 52 The surface area is 52 cm2.

Additional Example 1B: 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 1 cm Find the area of each view. bottom back right 8 + 8 + 6 + 8 + 8 + 6 = 44 The surface area is 44 cm2.

Draw each view of the figure. top front left Check It Out! Example 1A 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 1 cm Find the area of each view. bottom back right 8 + 8 + 4 + 8 + 8 + 4 = 40 The surface area is 40 cm2.

Draw each view of the figure. top front left Check It Out! Example 1B 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 1 cm Find the area of each view. bottom back right 8 + 9 + 6 + 8 + 9 + 6 = 46 The surface area is 46 cm2.

The lateral faces of a prism are parallelograms that connect the bases 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.

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 = 2B + Ph = 2( • 8 • 3) + (18)(10) 1 2 = 204 ft2

Check It Out! Example 2 Find the surface area of the figure to the nearest tenth. The figure is a triangular prism. S = 2B + Ph 7 cm = 2( • 7 • 6) + (21)(10) 1 2 7 cm 6 cm = 252 cm2 10 cm 7 cm

The lateral surface of a cylinder is the curved surface.

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 = 2pr2 + 2prh = 2p(42) + 2p(4)(6) = 80p in2  251.2 in2

Check It Out! Example 3 Find the surface area of the cylinder to the nearest tenth. Use 3.14 for p. 15 cm S = 2pr2 + 2prh 3 cm = 2p(152) + 2p(15)(3) = 540p in2  1695.6 cm2

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. Only the lateral surface needs to be covered. L = 2rh = 2(4)(11) Diameter ≈ 8 cm, so r ≈ 4 cm. = 88 ≈ 267.3 cm2

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r2 + 2rh The diameter is 6 ft, so r = 3 ft. = 2(32) + 2(3)(12) = 90 ft2  282.6 ft2

Lesson Quiz Find the surface area of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular prism 2. the cylinder 360 cm2 320.3 in2 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 in2