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Solving Prisms: Surface Area and Volume

Learn how to calculate the surface area and volume of prisms by scaling up dimensions. Explore different arrangements and their impact on surface area. Understand the relationships between dimensions and calculate volume changes with various scale factors.

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Solving Prisms: Surface Area and Volume

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  1. Unit: Filling and Wrapping Math CC7/8 – Be Prepared Journal: • Date: 1/31/2019 • Title: FW 1.4 Scaling Up 3) Sign off neighbor's HW from last night.  4) Warm Up: Write down what you know… On Desk: Turn In: Check Family Access. Are you missing anything? Complete yesterday’s labsheets 8 cubes and 27 cubes. Be ready to check! • In Your Planner: • HW: p. 18, #10 a-b, 26-28 • FW Unit Test-No Retakes • ISD common assessment- • Next Tues. and Wed.

  2. Tasks for Today • Warm up • Wrap up 1.2-1.3 Greatest and Least SA-patterns? • Lesson 1.4 – Scaling Up Prisms • Exit Ticket 1.3? • Begin HW?

  3. Warm Up If time…

  4. Warm Up The following polyhedron is a cube. Find the Surface Area. Front = 12 x 12 = 144 144 x 6 = 864 square feet Whycan I solve it this way?? 12 feet

  5. Possible Arrangements of 24 cubes

  6. Possible Arrangements of 8 cubes • Does it matter which order the dimensions are in? • Is (8 in x 1 in x 1 in) the same rectangular prism as (1 in x 1 in x 8 in), or (1 in x 8 in x 1 in) ? • Which arrangement had the mostsurface area? Why? • Which arrangement had the leastsurface area? Why? No! Yes!

  7. Possible Arrangements of 27 cubes Does it matter which order the dimensions are in? No! 27 x 1 x 1 1 x 27 x 1 1 x 1 x 27 Same SA and Volume!

  8. Answers to Lab Sheet • 8 cubes = 2 in x 2 in x 2in 27 cubes = 3 in x 3 in x 3 in • The name for these types of prisms is a cube. • 24 cubes = 2 in x 3 in x 4 in • The shape closest to a cube has the leastamount of surface area. • a. 12 in x 1 in x 1 in will have the most surface area because it is least like a cube. b. 3 in x 2 in x 2 in will have the least surface area because it is most like a cube.

  9. Adapted lesson *use blocks for demo • Calculate the Surface Area and the Volume of a 1 x 1 x 1 rectangular prism. • SA = 6 sq. in. • Vol = 1 cubic in. • What happens when you doubleonly the length? • (1 dimension) • What is the SA? • What is the Volume? SA = 10 sq. in. Vol = 2 cubic in.

  10. What happens when you double the lengthAND the width? (2 dimensions) • What is the SA? • What is the Volume? SA = 16 sq. in. Vol = 4 cubic in. • What happens when you double the length, the width, AND the height? (3 dimensions) • What is the SA? • What is the Volume? SA = 24 sq. in. Vol = 8 cubic in.

  11. What happens to the SA… • when you apply a scale factor of 2? • All 3 dimensions are multiplied by 2. • What is the relationship between the original SA and the new SA? • What is the relationship between the scale factor and how many times larger the SA is? • What happens to the Volume… • when you apply a scale factor of 2? • All 3 dimensions are multiplied by 2. • What is the relationship between the original Vol. and the new Vol.? • What is the relationship between the scale factor and how many times larger the Vol. is?

  12. Together as a class… Double any ONE of the dimensions – length, width or height Triple any ONE of the dimensions – length, width or height Halving any ONE of the dimensions – length, width or height

  13. V = 4 x 8 x 12 = 384 cubic in. V = (V x 2 x 2 x 2) V = (V x 1.5 x 1.5 x 1.5) V = (V x 0.5 x 0.5 x 0.5) You can find these answers by multiplying the original box volume by the 3 f This is read, “Scale Factor cubed”.

  14. Work in Groups… If Time… 25 x 200 = 5,000 cm or 50 meters long 3,000 30 m = 3,000 cm 15 cm = 200

  15. If Time… 3 2 2 3 2 3 2 3 x 20 cm 800,000 cm or 80 m 200 100 cm 200 800,000,000 cm or 800 m x = = 200 * 200 because you’re multiplying two dimensions 200 * 200 * 200 because you’re multiplying three dimensions

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