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Academic Skills Advice
Summary
Formulae
Substitution in formulae:
Substitution means replacing the letters in a formula with the given values.
Example:


( = 3.14,  = radius)
Volume of sphere =  
Formula:
Find the volume of a sphere with radius 8cm.
4
 3
Volume =
Replace  with 3.14 &  with 8:
Volume = 3 x 3.14 x 8 x 8 x 8
Tidy up:
Volume = 2143.57cm2.
3
4
(this means 3 ×  ×  ×  × ).
Original formula:
4
Rearranging Formulae:
As with linear equations you can think that:
When something crosses to the other side of the equals sign it does the “opposite”.
E.g. + becomes -, x becomes ÷ and vice versa.
Example:

Given that  =


, make  the subject of the formula.
3 2
Original formula:
=
÷5 changes side and becomes x5:
5 = 3 2
x3 changes side and becomes ÷3:
5
3
5
= 2
5
Power changes side and becomes root:
√
Rewrite with subject on the left:
 = √
© H Jackson 2011 / ACADEMIC SKILLS
3
=

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