Dimensions & Formulae AQA Module 5

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!

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

= 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

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

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

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

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

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