Lesson 2: Surface Area of 3. D Shapes. STANDARDS (CCSS AND NCTM)Grade 7: Geometry (CCSS 7. G. B. 4 and 6)Grades 6–8: Make Sense of Problems, Reason Abstractly and Quantitatively, Construct Viable Arguments, Attend to Precision, and Look for and Make Use of Structure (CCSS MP1- 3 and 6- 7); NCTM Geometry. ![]() Download a comprehensive Standards Chart. OBJECTIVEIn this lesson, students will understand formulas used to measure the surface area of these basic 3. D shapes: a rectangular prism, a cylinder, and a square pyramid. MATERIALSDIRECTIONSTime Required: 3. Draw a rectangular prism on the board with these measurements: height = 3 feet, length = 4 feet, and width = 5 feet. Ask students to calculate the area of one of the surfaces, say 5 x 4 = 2. ![]() ![]() Repeat for the other surfaces. Point out that opposite surfaces have the same area. Show students the surface area formula for rectangular prisms on the poster: SA= 2 (l . Explain to them that the surface area of 3. D objects is measured in square units, just like the area of 2. D objects, and is the sum of all of the 3. D object's 2. D surfaces. Demonstrate how to calculate total surface area for the rectangular prism you have drawn. Now draw a cylinder and mark the dimensions with the radius at 3 feet and the height at 4 feet. Indicate that the surface area for a cylinder equals the area of the two bases plus the area of the surface between the bases. Demonstrate this to your class by using a rolled- up piece of paper to create a cylinder; use two paper circles (cut out beforehand) to fill in the bases. When you unroll the paper, students will see that the surface between the two bases is a rectangle when . Show students the surface area formula for cylinders on the poster: SA= (2 . Finally, draw a square pyramid on the board and mark the dimensions with a base length of 6 feet and a base width of 6 feet. Show the slant height as 5 feet by drawing a perpendicular line from the center of one of the base sides to the top of the pyramid. The square pyramid has a base area (BA) measurable by l . Show students the surface area formula for square pyramids on the poster, SA= (BA) + 1/2 P . This formula adds together the area of the base with the area of the four triangular sides of the square pyramid. The P in the formula refers to the perimeter of the base. The answer is 3. 6 + 1/2 . Guided Practice: In groups or in pairs, ask students to calculate surface areas for: A rectangular prism with the following measurements: length 3 meters, width 7 meters, and height 5 meters . The perimeter of the base = 4 x 6. ![]() The surface area of the square pyramid is 3,6. Independent Practice: Distribute Worksheet 2 Printable (PDF). Tell students they should complete all the questions. You may want to take some extra time in class to go over the bonus question, which introduces the formula for measuring the surface area of a cone . 12 cm 3) 15.6 in 4) 7 cm 5) 8 in 6) 10 mi 7) A sphere with a diameter of 6.2 in. Check for Understanding: Go over all correct answers as a class, referring to the Worksheet Answer Key (PDF). Use the following printables as extensions to Lesson 2: Program Links. Worksheet 3 Class: Volume of Sphere = Volume of hemisphere = Surface area of Sphere = 4. The surface area of a sphere is the same as the lateral surface area of a cylinder with the same radius and a height of 2r. The area of this cylinder is 2. LEARNING GOALS By the end of this unit, you should be able to: Identify and use the correct formula for calculating the surface area (SA) of various prisms (cubes, rectangular prisms, etc. Identify and use the. 5) Find the volume of an open hemisphere whose external surface area is 1762 cm. Give your answer to 3 significant figures. ![]()
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