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Solving Problems with Surface Areas and Volumes

Learn how to solve problems involving surface areas and volumes of 3-dimensional figures, including maximization, scale, and increment problems.

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Solving Problems with Surface Areas and Volumes

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  1. Tuesday, 20190409 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 : ACT • 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. ACT Bellwork 20180313 Tuesday

  3. 1 Bellwork: ACT, Tuesday, 20190409

  4. 2 Bellwork: ACT, Tuesday, 20190409

  5. 3 Bellwork: ACT, Tuesday, 20190409

  6. 4 Bellwork: ACT, Tuesday, 20190409

  7. 5 Bellwork: ACT, Tuesday, 20190409

  8. Surface Area

  9. EQ 36. How do we compute the perimeter of simple composite geometric figures with unknown side lengths? EQ 38. How do we solve problems involving surface areas and volumes of 3-dimensional figures, including maximization, scale, and increment problems?

  10. Vocabulary for Surface Area (SA) • Surface area - The sum of the areas of the faces of a three-dimensional figure. • Base-In a prism or a cylinder, it is one of two Parallel and Congruent sides. • Rectangular Prism -A three-dimensional (3D) shape with 6 rectangular faces. Triangular prism -is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. Face -A flat surface on a three-dimensional (3D) shape.

  11. Day 1 - Surface Area of Prisms Surface Area = The total area of the surface of a three-dimensional object (Or think of it as the amount of paper you’ll need to wrap the shape.) Prism =A solid object that has two identical ends and all flat sides. We will start with 2 prisms – a rectangular prism and a triangular prism. Triangular Prism Surface area=bh+2ls+lb Rectangular Prism SA = 2lw + 2lh + 2wh

  12. Surface Area (SA) of a Rectangular Prism Like dice, there are six sides (or 3 pairs of sides)

  13. Prism net - unfolded

  14. Add the area of all 6 sides to find the Surface Area. 6 - height 5 - width 10 - length

  15. 6 - height SA = 2lw + 2lh + 2wh 5 - width 10 - length SA = 2lw + 2lh + 2wh SA = 2 (10 x 5) + 2 (10 x 6) + 2 (5 x 6) = 2 (50) + 2(60) + 2(30) = 100 + 120 + 60 = 280 units squared

  16. Practice 12 ft 10 ft 22 ft SA = 2lw + 2lh + 2wh = 2(22 x 10) + 2(22 x 12) + 2(10 x 12) = 2(220) + 2(264) + 2(120) = 440 + 528 + 240 = 1208 ft squared

  17. Surface Area of a Triangular Prism • 2 bases (triangular) • 3 sides (rectangular)

  18. Unfolded net of a triangular prism

  19. 2(area of triangle) + (Area of rectangles) Area Triangles = ½ (b x h) = ½ (12 x 15) = ½ (180) = 90 Area Rect. 1 = b x h = 12 x 25 = 300 Area Rect. 2 = 25 x 20 = 500 15ft SA = 90 + 90 + 300 + 500 + 500 SA = 1480 ft squared

  20. Practice 7 cm 9 cm 8 cm 10 cm

  21. 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

  22. End of Day 1

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