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8.8: Optimum Volume and Surface Area

8.8: Optimum Volume and Surface Area. MPM1D1 March 2008 J. Pulickeel. What Is Optimal Area and Volume?. When we are talking about optimal area and volume we want to MAXIMIZE the VOLUME and MINIMIZE the AREA. 5. 5. 6. 6. 7. 7. 40. 10. 27.8. 20.4. 10. V = 1000 u 3.

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8.8: Optimum Volume and Surface Area

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  1. 8.8: Optimum Volume and Surface Area MPM1D1 March 2008 J. Pulickeel

  2. What Is Optimal Area and Volume? When we are talking about optimal area and volume we want to MAXIMIZE the VOLUME andMINIMIZE the AREA 5 5 6 6 7 7 40 10 27.8 20.4 10 V = 1000 u3 V = 1000 u3 V = 1000 u3 V = 1000 u3 SA = 600 u2 SA = 739.2 u2 SA = 850 u2 SA = 669.2 u2 10

  3. Which shape is the most Optimal? • A SPHEREhas the largest volume and smallest surface area. • A 3D shape that is CLOSEST to the shape of sphere will have the next largest volume • A CUBE is the rectangular prism with the largest volume

  4. Which shape would have the optimal Volume if the Surface Area is the same? 1 3 2

  5. How could I increase the volume of these shapes without changing the surface area? 2 3 1 The height and diameter should be the same Change this cylinder into a cylinder that is closer to a sphere/cube Change this rectangular prism into a cube Change this oval into a sphere D = 2r=h d r l w h h h l l l

  6. Find the maximum volume of a cube with a surface area of 1200cm2 SACUBE = 6l2 SACUBE = 1200cm2 VCUBE = l3 1200cm2 = 6l2 VCUBE = (14.14cm)3 1200cm2= 6l2 6 6 VCUBE = 2828.4cm3 200cm2 = l2 14.14cm = l

  7. Find the maximum volume of a cylinder with a surface area of 1200cm2 • We need a cylinder where the height is equal to the diameter, and the SA must equal 1200cm2

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