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Mastering Surface Area and Volume Calculations with 3D Figures

Learn how to solve problems involving surface areas and volumes of 3-dimensional figures, maximization, scale, and increment scenarios. Understand concepts, formulas, and application examples for cylinders. Practice and grasp the calculations effectively.

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Mastering Surface Area and Volume Calculations with 3D Figures

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  1. Wednesday, 20190410 Essential Question • EQ38 How do we solve problems involving surface areas and volumes of 3-dimensional figures, including maximization, scale, and increment problems? WW#4 • Store your phones • Find your seat by Letter & Number • Calculator • Agenda Senior Math • Bellwork : N2K • EQ37 Surface Area • Exit Ticket Celebrate your Assistant Principal This WEEK! It’s always a great day to be a Wolverine! • Remain in seat until bell rings. Teacher Dismisses NOT the bell.

  2. N2K Bellwork: Wednesday, 20190410 4 corners Critical Thinking activity The N2K is in labeled folders around the room. Please find your A, B, C, or D to answer the questions with your group. ***See the yellow sticky note on your desk to find your assigned folder questions. 2nd Question: Students select multiple correct answers from the many options.

  3. A N2K: Bellwork: Wednesday, 20190410 Match each formula to the correct geometric figure.

  4. B N2K: Bellwork: Wednesday, 20190410 Match each formula to the correct geometric figure.

  5. C N2K: Bellwork: Wednesday, 20190410 Match each formula to the correct geometric figure.

  6. D N2K: Bellwork: Wednesday, 20190410 Match each formula to the correct geometric figure.

  7. 19.4 m2 261 in2 400 in2 268 in2

  8. DAY 2Surface Area of a Cylinder

  9. Bellwork: Tuesday, 10/13/2015

  10. EQ 37. How do we compute the perimeter of simple composite geometric figures with unknown side lengths? EQ 39. How do we solve problems involving surface areas and volumes of 3-dimensional figures, including maximization, scale, and increment problems?

  11. Review • Surface area is like the amount of paper you’ll need to wrap the shape. • You have to “take apart” the shape and figure the area of the parts. • Then add them together for the Surface Area (SA)

  12. Parts of a cylinder A cylinder has 2 main parts. A rectangle and A circle – well, 2 circles really. Put together they make a cylinder.

  13. The Soup Can Think of the Cylinder as a soup can. You have the top and bottom lid (circles) and you have the label (a rectangle – wrapped around the can). The lids and the label are related. The circumference of the lid is the same as the length of the label.

  14. Area of the Circles Formula for Area of Circle A=  r2 = 3.14 x 32 = 3.14 x 9 = 28.26 But there are 2 of them so 28.26 x 2 = 56.52 units squared

  15. The Rectangle This has 2 steps. To find the area we need base and height. Height is given (6) but the base is not as easy. Notice that the base is the same as the distance around the circle (or the Circumference).

  16. Find Circumference Formula is C =  x d = 3.14 x 6 (radius doubled) = 18.84 Now use that as your base. A = b x h = 18.84 x 6 (the height given) = 113.04 units squared

  17. Add them together Now add the area of the circles and the area of the rectangle together. 56.52 + 113.04 = 169.56 units squared The total Surface Area!

  18. Formula SA = (d x h) + 2 (r2) Label Lids (2) Area of Rectangle Area of Circles

  19. PracticeFind the surface area of this cylinder. Be sure you know the difference between a radius and a diameter! SA = ( d x h) + 2 ( r2) = (3.14 x 22 x 14) + 2 (3.14 x 112) = (967.12) + 2 (3.14 x 121) = (967.12) + 2 (759.88) = (967.12) + (759.88) = 1728 cm2 SA = ( d x h) + 2 ( r2)

  20. 11 cm 7 cm PracticeFind the surface area of this cylinder. Be sure you know the difference between a radius and a diameter! SA = ( d x h) + 2 ( r2) = (3.14 x 11 x 7) + 2 ( 3.14 x 5.52) = (241.78) + 2 (3.14 x 30.25) = (241.78) + 2 (94.985) = (241.78) + (189.97) = 431.75 cm2

  21. Exit Ticket: Composition Book • True/False Identify whether the following statements are true or false. • ___ 14. A rectangular prism has 3 pairs of identical sides. • a. True • b. False • ___ 15. The surface area of an object is the total area of the exterior surface of a • solid. • a. True • b. False

  22. End of Day 2

  23. Exit Ticket • True/False Identify whether the following statements are true or false. • ___ 14. A rectangular prism has 3 pairs of identical sides. • a. True • b. False • ___ 15. The surface area of an object is the total area of the exterior surface of a • solid. • a. True • b. False

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