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Math Adventure: Unlock the Secrets of Itinerary 5

Embark on a mathematical journey into a parallel universe of shapes and formulas in this interactive experience. Master area calculations for 3D shapes in Mission 1 - Surface Area of Prisms and Cylinders.

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Math Adventure: Unlock the Secrets of Itinerary 5

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  1. Feel The Math

  2. Welcome ! My name is Box Muddler. I will be your guide throughout this mathematical experience. You are about to enter a parallel universe. You must successfully navigate through this world, mastering the challenges that it presents. Good luck, be careful, and trust no one.

  3. What is this Place? Itinerary 5 is a land of mysterious, adventure, and misfortune. It is extremely complex, yet straight forward. Take the area formulas from grade 7 and 8 and used cautiously on the three dimensional shapes you can find Volume and Surface Area.

  4. Where do you want to go today? • Mission 1 • Mission 2 • Mission 3 • Mission 4 • Mission 5 • Mission 6 • Mission 7

  5. Mission 1 Mission for 1: To successfully find the surface area of prisms and cylinders. Vocabulary: Lateral area & total (surface) area, Formulas: L.A. = PbH T.A. = L.A. + Abases

  6. Terminology Surface area is the total area of the surface of a 3-dimensional figure. In other words, surface area is the amount of cardboard it takes to make a box, or the amount of wrapping it takes to cover a present.

  7. Terminology Lateral area is the area of the lateral sides of a 3-dimensional figure. In other words, lateral area is just the area of the sides of a figure. For example, lateral area is the surface I would paint if I had to paint the sides of a bucket.

  8. Formula for L.A. The formula for the lateral area (L.A.) of a right prism or cylinder is the product of its height H and the perimeter p of its base. L.A. = Pb  H

  9. Important Formulas / Reminders • Area of Circle: • A = πr2 ( = 3.14) • Circumference of circle • C = 2πr • Perimeter of circle = ? • P or circle = C & Perimeter of Base = C • If Radius = 5; diameter = 10 (d=2r) • Area of Rectangle = length (l) x width (w) • Perimeter of Rectangle = 2l + 2w r =5 3 7

  10. Example Find the lateral area of a right cylinder with a height of 5 and a base radius of 3. LA = PbH = 2  r  H = 2  (3) (5) = 94.2 units2 Remember… area is measured in square units

  11. You try it! What’s the lateral area of a rectangular prism to the left?

  12. The answer you have selected is incorrect. The correct answer was 252. Click on “show me” to see how this problem should be done.

  13. Here is your Answer... LA = PbH = [2l + 2w]  H = [(2)(6) + (2)(3)]  14 = [12 + 6]  14 = 252 units2

  14. You got it. Onto to the next concept!

  15. Formula for T.A. The formula for the surface (T.A.) of a right prism or cylinder is the sum of its lateral area and twice the area of its base. T.A. = L.A. + Abases

  16. example Find the total area of a right cylinder with a height of 5 and a base radius of 3. T.A. = L.A. + Abases = 2rh + 2r2 = 2 (3)(5) + 2 (3)2 = 94.2 + 56.52 = 150.72 units2

  17. You try it! What’s the surface area of the right cylinder to the left? 100.50 251.3 351.68 603.20

  18. Not bad hot shot! Click next to move on.

  19. The answer you have selected is incorrect. The correct answer was 351.8. Click on “show me” to see how this problem should be done.

  20. Here is your Answer... T.A. = L.A. + Abases = 2rH + 2 r2 = 2 (4)(10) + 2 (4)2 = 351.68 units2

  21. One more for mission 1 What is the surface area of an open box with a 12 X 17 base and a height of 7? • T.A. = L.A. + Abase • T.A. = 2(l) + 2(w)h+lw • = [2(12)+2(17)]  7 + (12) (17) • = (58) (7) + 204 = 610 units2

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