1. Dimensions & Formulae
AQA Module 5

2. Dimensions
We can tell if a formula gives a Length, an Area or a Volume
i.e. whether it has 1, 2 or 3 dimensions
Or NONE of these!

3. = L How do we do this? L = Length Break down the formula
Eliminate ANY numbers
r is radius, a length L
L = Length

4. = L2 How do we do this? L2 = Length x Length = Area
Break down the formula
= L2
Eliminate ANY numbers
r is radius, a length L
L2 = Length x Length = Area

5. = (L+L)L = (2L)L = LxL = L2 How do we do this?
L2 = Length x Length = Area

6. L3 = Length x Length x Length = Volume
How do we do this?
= L2xL+LxLxL
= L3+L3
= 2L3
= L3
L3 = Length x Length x Length = Volume

7. L3 = Length x Length x Length = Volume
How do we do this?
= L2xL
= L3
L3 = Length x Length x Length = Volume

8. Cannot have more than 3 dimensions! This formula represents NOTHING
How do we do this?
= L2xLxL
= L4
Cannot have more than 3 dimensions!
This formula represents NOTHING
Inconsistent

9. Cannot have a MIXTURE of dimensions! This formula represents NOTHING
How do we do this?
= L x L + L + L x L
= L2 + L + L2
= 2L2 + L
= L2 + L
Cannot have a MIXTURE of dimensions!
This formula represents NOTHING
Inconsistent