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03.01.2018

Discover the importance of surface area, learn how to calculate it, and explore applications in real-world scenarios. From prisms and pyramids to cylinders and cones, delve into the realm of three-dimensional shapes.

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03.01.2018

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  1. 03.01.2018 Agenda Ticket in the Door Drop everything and Read! • Ticket in the door • Current Lesson; Surface Area • Wrap-up • Unit 4 Test has been rescheduled to Monday 03.05.2018

  2. Surface Area

  3. SURFACE AREA Essential Questions • Why should you learn about surface area? • Is it something that you will ever use in everyday life? • If so, who do you know that uses it? • Have you ever had to use it outside of math?

  4. Surface Area • What does it mean to you? • Does it have anything to do with what is in the inside of the prism.? • Surface area is found by finding the area of all the sides and then adding those answers up. • How will the answer be labeled? • Units2 because it is area!

  5. Define Surface Area: • The amount of material it would take to • cover a 3D shape. • The area of everything on the outside • of a space figure measured in square • units

  6. Types of space figures: • Prism • Pyramid • Cylinder • Cone • Sphere a space figure with two parallel sides that are congruent a space figure with only one base; its faces are triangles a space figure with a curved surface and two congruent parallel bases that are circles a space figure with one circular base and a curved surface that comes to a point a space figure with no bases and only curved surfaces

  7. Surface Area of a Prism/Pyramid Sum of the area of its faces • Steps: • Draw and label all of the faces • Find the area of each face • Add all of the faces together

  8. Find the surface area of the following prism: 8 2 of them 8 cm 2 of them 5 7 6 A = (b)(h) A = ½ (b)(h) 5 cm = (5)(8) 7 cm = ½ (6)(7) = 80 cm2 = 40 (2) = 21(2) = 42 cm2 6 cm A = (b)(h) 5 = (5)(6) 6 = 30 cm2 Total Area = 42 + 80 + 30 = 152 cm2

  9. Find the surface area of the following Square Pyramid: 10 4 of them 12 cm 12 10 10 cm 10 A = (b)(h) A = ½ (b)(h) = (10)(10) = ½ (10)(12) = 100 cm2 = 60(4) = 240 cm2 Total Area = 240 + 100 = 340 cm2

  10. Surface Area of a Cylinder • Steps: • Identify the radius and height • Addr and h into equation

  11. Find the surface area of the following prism: = 4 r = 8/2 8cm h = 14 14cm

  12. Surface Area of a Cone • Steps: • Identify the radius and slant height • Addr and s into equation

  13. Find the surface area of the following prism: = 2 r = 4/2 2.6 m s = 2.6m 4 m

  14. Surface Area of a Sphere • Steps: • Identify the radius • Add r into equation

  15. Find the surface area of the following prism: = 4.5 r = 9/2 9 in

  16. B C 5 in A 6 4 Rectangular Prism How many faces are on here? 6 Find the area of each of the faces. Do any of the faces have the same area? A = 5 x 4 = 20 x 2 =40 If so, which ones? B = 6 x 5 = 30 x 2 = 60 C = 4 x 6 = 24 x 2 = 48 Opposite faces are the same. 148 in2 Find the SA

  17. Cube Are all the faces the same? YES A How many faces are there? 4m 6 Find the Surface area of one of the faces. 4 x 4 = 16 Take that times the number of faces. X 6 96 m2 SA for a cube.

  18. Triangular Prism How many faces are there? 4 5 5 How many of each shape does it take to make this prism? 10 m 3 2 triangles and 3 rectangles = SA of a triangular prism Find the surface area. Start by finding the area of the triangle. x 2= 12 4 x 3/2 = 6 How many triangles were there? 5 x 10 = 50 = front 4 x 10 = 40 = back 3 x 10 = 30 = bottom 2 Find the area of the 3 rectangles. SA = 132 m2 What is the final SA?

  19. Triangular Prisms • Use the same triangular prism we used before. Let’s us the formula this time. 2B + LSA=SA • Find the area of the base, which is a triangle because it is a triangular prism. You will need two of them. • Now, find the perimeter of that same base and multiply it by how many layer of triangles are in the picture. That is the LSA. • Add that to the two bases. Now you should have the same answer as before. • Either way is the correct way.

  20. Cylinders What does it take to make this? 6 10m 2 circles and 1 rectangle= a cylinder 2B + LSA = SA 2 B 3.14 x 9 = 28.26 X 2 = 56.52 + LSA(p x H) 3.14 x 6 =18.84 x 10 = 188.4 SA = 244.92

  21. Reference • https://bj041.k12.sd.us/power%20points/surface%20area.ppt • www.ecusd7.org/ehs/ehsstaff/jlunte/.../5.6%20surface%20area%20powerpoint.ppt

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