1. Year 9 Dimensional Analysis
Dr J Frost
Objectives: Identifying whether a formula represents a length, area or volume.
Last modified: 19th February 2014

2. Circumference of a circle.
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. 2πr πr(r+l) Length, area or volume? A length An area
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. length + length = length
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)?
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? ? ?
volume ? ? ?

7. Exercise 1                      
Copy this table out and put a tick in the correct column.
(all variables r, h, b are lengths)
Expression
Length
Area
Volume
None of these
2rh
πr + 4h
(r+h)2 3b
b3 + rh
πr2(h + r)
bhr_
(b+h)  ? ?   ? ?   ? ?  ?  ?   ? ?   ? ?   ?  ? ?   ?  ? ?   ? ?   ?  ? ?   ?

8. Questions ? ? ? ? ? ? 1 Which expression could represent an area?
3b + r2 h
Click to REVEAL ANSWER
b + rh h(3+r) πb2 + 4h bh + πr2 2
Which expression could NOT represent a volume?
Click to REVEAL ANSWER
5h4
b+r
4b2h πr2(h+2) (h+2r) 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 ?