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The Science of Size and Shape

The Science of Size and Shape. Definitions. Surface Area : The measure of how much exposed area a solid object has, expressed in square units (x 2 ).

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The Science of Size and Shape

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  1. The Science of Sizeand Shape

  2. Definitions • Surface Area: The measure of how much exposed area a solid object has, expressed in square units (x2). • Volume: How much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies and is expressed in cubed units (x3). • Ratios (Surface Area:Volume) or Fractions (SA/V) make comparisons between two things.

  3. 1.Out of these three, solid, 3D shapes, which has the biggest surface area?   2. Which has the biggest volume? 3. Which has the biggest surface area to volume ratio? 4.Which of these animals has the biggest surface area to volume ratio? A. Giraffe       B. Elephant        C. Horse        D. Hamster        E. Don’t know 5.How is the job of the mitochondria improved by having an inner membrane with many folds?

  4. What shape does your body take when you are hot? What shape does your body take when you are cold?

  5. SA:V ratios determine the size and shapes of animals Why are the shapes of these rabbits’ ears so different? Which has the higher SA:V ratio? Why?

  6. SA:V ratios determine the size and shapes of plants Do these plants have low or high SA:V ratios? Why do they have this shape?

  7. How does Surface Area Relate to Volume? • If SA increases will V increase? • If SA decreases will V decrease? Will the increase or decrease be at the same rate? Talk to your neighbor about your answersand write your hypotheses on your worksheet in a full sentence. (for example: As surface area increases volume will…)

  8. Equations for Surface Area: Rectangle: 2(wh) + 2(lw) + 2(lh) Cube: 6x2 Equations for Volume: Rectangle: lwh Cube: x3 A. B. C. A. Surface Area = 2(2*4 + 8*2 + 8*4) = 112 units2 Volume = 8*2*4 = 64 units3 C. Surface Area = 2(2*16 + 2*2 + 2*16) = 136 units2 Volume = 2*2*16 = 64 units3 B. Surface Area = 6*42 = 96 units2 Volume = 43 = 64 units3

  9. Rates of change as size increases As size increases (as seen on the X axis) what happens to SA and V? Do SA and V change at the same rate? Which changes faster with increasing size? What happens to the SA:V ratio as size increases? How does this change your hypotheses?

  10. Long and skinny = low SA:V ratio Protists Neuron Cell

  11. SA:V ratios and size Size At size 2 the SA:V ratio is 75:25 or 3:1 At size 3 the SA:V ratio is 66:33 or 2:1 At size 6 the SA:V ratio is 50:50 or 1:1 At size 9 the SA:V ratio is 40:60 or 2:3 At size 10 the SA:V ratio is 33:66 or 1:2 The SA:V ratio decreases with increasing size.

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