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Unit 7: Solid Figures and Measurement

Learn to derive and apply formulas for the surface area of prisms and cylinders using 2D figures, manipulatives, and nets. Practice computing surface area and solving real-world problems. Enhance your understanding of geometric concepts and boost your problem-solving skills efficiently. Finish nets with scissors and glue in just 5 minutes for a hands-on learning experience.

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Unit 7: Solid Figures and Measurement

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  1. Unit 7: Solid Figures and Measurement Now’s the time to SHAPE UP!!

  2. Warm-Ups Jim-Bob’s cousin Billy-Bob comes into town to visit. They go see the Monster Truck Extravaganza. Tickets are $38.25 each and they buy two. They buy two packs of pork rinds at $2.50 a bag, two root beers at $1.50 each, and two foam fingers at $6.00 each. Jim-Bob also buys a “LOVE STINKS” t-shirt for $12.00. Tax is 6%. How much did they spend?

  3. Finish Net Construction • Get scissors and glue to finish nets • You have only 5 minutes to finish.

  4. Surface Area What am I Learning Today? How will I show that I learned it? Derive a formula for the surface area of prisms and cylinders using 2D figures, manipulatives and nets Compute surface area using formulas Solve application problems involving surface area

  5. Formula Review Area of a rectangle: l x w 3 cm A = 3 x 1 = 3 cm2 1 cm

  6. Vocabulary • Surface area: The sum of the area of the faces of a solid figure

  7. Questions Notes Questions Answers What is the formula for the surface area of a prism ? SA =(2 x l x w) + (2 x w x h) + (2 x l x h) 2 m SA = (2 x l x w) + (2 x w x h) + (2 x l x h) SA = (2 x 3 x 2) + (2 x 2 x 5) + (2 x 3 x 5) SA = 12 + 20 + 30 SA = 32 + 30 = 62 m2 5 m 3 m What is the formula for the surface area of a cube? SA = 6s2 SA = 6 x 32 = 6 x 9 SA = 54 in2 SA = 6s2 3 in.

  8. Where does the formula come from? There is a front, back, top, bottom, left, and right view to every rectangular prism. The surface area of a prism is nothing more than the sum of all the areas of these rectangles.

  9. SA = 2(lw) + 2(hl) + 2(hw) SA = 2 x 8 x 6 + 2 x 7 x 8 + 2 x 7 x 6 SA = 2 x 48 + 2 x 56 + 2 x 42 SA = 96 + 112 + 48 SA = 208 + 48 SA = 292 ft² Surface Area of a Prism 7 ft 6 ft 8 ft Now you try: What is the surface area of a rectangular prism with a length of 6 ft, a width of 5 ft, and a height of 7 ft ? SA = 2(6 x 5) + 2(7 x 6) + 2(7 x 5) = 214 ft2

  10. Add the areas of each face. Can we find the surface area of a prism using its net? A: A = 6  3 = 18 A B: A = 6  3 = 18 6 in. 6 in. 3 in. 3 in. C: A = 11  6 = 66 11 in. D: A = 11  6 = 66 C E D F E: A = 11  3 = 33 B F: A = 11  3 = 33 SA = 2(18) + 2(66) + 2(33) 36 + 132 + 66 = 234 The surface area is 234 in2.

  11. Plug and Chug Practice Find the surface area of the following solids using the appropriate formula. 1) 2) The side of a cube is 2 cm. What is its surface area? SA = 188 in2 12 in. 2 in. 5 in. SA = 24 cm2

  12. White Boards Practice Area of a Rectangle and Surface Area of a Rectangular Prism: http://www.thatquiz.org/tq-4/?-j20a1-la-n35-p2kc0

  13. Formula Review Area of a circle: Circumference of a circle: πr2 10 mi A = 3.14 x 102 = 3.14 x 100 = 314mi2 2πr 6 mm C = 2 x 3.14 x 6 = 6.28 x 6 = 37.68 mm2

  14. Vocabulary • Radius: The length of the line segment with one endpoint at the center of the circle and one endpoint on the circle. It is half the diameter. • Pi: The ratio of the circumference of a circle and the length of its diameter. TT= 3.14

  15. Questions Notes Questions Answers What is the surface area of a cylinder? SA = 2TTr2 + 2TTrh 2 cm SA = 2TTr2 + 2TTrh SA = 2TT x 2 + 2TT x 2 x 4 SA = 2 TT x 4 + 16TT SA = 8TT + 16TT SA = 24TT cm OR SA = 2 x 3.14 x 22 + 2 x 3.14 x 2 x 4 SA = 6.28 x 4 + 6.28 x 8 SA = 25.12 + 50.24 = 75.36 cm2 4 cm 4 cm

  16. Where does the formula come from? A cylinder has three surfaces: a top, bottom, and middle. The top and bottom, which are circles, each have an area of πr2. When the cylinder wall is completely open, we see that the circumference of the circle becomes the length of the rectangle. The dimensions of the rectangle are the circumference, C = 2πr, and the height of the cylinder, h.

  17. SA = 2πr² + 2πrh SA = (2 x 3.14 x 3²) + (2 x 3.14 x 3 x 5) SA = (6.28 x 9) + (6.28 x 15) SA = 56.52 + 94.2 SA = 150.72 in² Surface Area of a Cylinder 3 in 5 in Now you try: Find the surface area of a cylinder that has a height of 5 ft and a radius of 2 ft. SA = (2 x 3.14 x 2²) + (2 x 3.14 x 2 x 5) = 37.68 ft2

  18. Plug and Chug Practice Find the surface area of the following solids using the appropriate formula. 1) 2) You design an oatmeal container as a cylinder with a radius of 2 in. and a height of 22.8 in. What is its surface area? 4 ft. SA = 88π ft2 SA = 276.32 ft2 7 ft. SA = 99.2 π in2 SA = 312 in2

  19. White Boards Practice Surface Area of a Circle and a Cylinder: http://www.thatquiz.org/tq-4/?-j240g-la-n35-p0

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