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8.8: Optimum Volume and Surface Area
MPM1D1 March 2008 J. Pulickeel
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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 40 6 27.8 7 20.4 10 V = 1000 u3 V = 1000 u3 V = 1000 u3 V = 1000 u3 SA = 600 u2 SA = u2 SA = 850 u2 SA = u2
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Which shape is the most Optimal?
A SPHERE has 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
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Which shape would have the optimal Volume if the Surface Area is the same?
1 3 2
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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 h d h l l w h r
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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 = cm3 200cm2 = l2 14.14cm = l
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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 Height (cm) Diameter(cm) Equal to height Radius (cm) ½ the height SA = 2πr2 + h(2πr) This has to equal 1200cm2 Volume (cm3) V = hπr2
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