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

2. Starter – What does it represent? What are each of these formulae used for? πr3πr3 4343 πr2hπr2h 2πr2πr 4πr24πr2 π r(r+l) Volume of sphere Circumference of a circle. h r r Volume of cylinder Surface area of sphere r r l Surface area of a cone. ? ? ? ? ?

3. 2πr2πr π r(r+l) A length An area Length, area or volume? Is there are way, just by looking at the formula, whether it represents a length, area or a volume?

4. 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) Rules of Dimensions 

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

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

7. Exercise 1 (all variables r, h, b are lengths) ExpressionLengthAreaVolumeNone of these 2rh πr + 4h (r+h) 2 3b b 3 + rh πr 2 (h + r) bhr_ (b+h) Copy this table out and put a tick in the correct column.  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ?  ? ? ? ? ? ? ?

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