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Year 9 Dimensional Analysis

Year 9 Dimensional Analysis. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Objectives: Identifying whether a formula represents a length, area or volume. Last modified: 19 th February 2014. Starter – What does it represent?. What are each of these formulae used for?. ?. ?. r. 4 3.

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Year 9 Dimensional Analysis

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  1. Year 9 Dimensional Analysis Dr J Frost (jfrost@tiffin.kingston.sch.uk) Objectives: Identifying whether a formula represents a length, area or volume. Last modified: 19th February 2014

  2. Starter – What does it represent? What are each of these formulae used for? ? ? r 4 3 πr3 4πr2 Volume of sphere Surface area of sphere ? ? πr(r+l) Volume of cylinder πr2h h l r ? 2πr r r Circumference of a circle. Surface area of a cone.

  3. Length, area or volume? Is there are way, just by looking at the formula, whether it represents a length, area or a volume? 2πr A length πr(r+l) An area

  4. Rules of Dimensions ! ? length + length = length length × length = area ? length × length = length length ? ? length × area = volume ? constant × length = length (This makes sense if you think about it. e.g. If I walk 3 times as far as 2km, I’ve walked 6km, i.e. 3 x 2km = 6km. i.e. constant x length = length)

  5. ? • length + area = (no meaningful dimension) (When we add/subtract values, they have to be of the same dimensions/units) constant + length = (no meaningful dimension) ? (It doesn’t make sense for example to have “3cm + 5”) volume = length area ? And one last slightly trickier one... length = constant length + length ?

  6. Quickfire Test Your Understanding ? ? ? ? ? ?

  7. Exercise 1 Copy this table out and put a tick in the correct column. (all variables r, h, b are lengths)  ?  ?  ?  ?  ?  ?  ?  ? ?   ? ?   ? ?  ?   ? ?   ? ?   ? ?   ? ?   ?  ?

  8. Questions 1 Which expression could represent an area? 3b + r2 h Click to REVEAL ANSWER b + rhh(3+r) πb2 + 4h2bh+ πr2 2 Which expression could NOT represent a volume? Click to REVEAL ANSWER 5h4 b+r 4b2h πr2(h+2) (h+2r)3 0.5 b2h Given that h and r are both lengths, determine the dimensions of the following, whether a length, area, volume or none of these. 3 ? ? a d ? e ? b ? c f ?

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