Rearranging Formulae

The area of a circle formula tells us that A=\pi r^2. Let’s rearrange that to make r the subject. Right now, A is the subject.

    \begin{align*}A&=\pi r^2 \\ \frac{A}{\pi}&=r^2 &\text{divide by }\pi \\ \pm\sqrt{\frac{A}{\pi}}&=r &\text{square root both sides} \\\sqrt{\frac{A}{\pi}}&=r &\text{reject negative as radius is a positive value} \\ r&=\sqrt{\frac{A}{\pi}} &\text{write with r on the left}\end{align*}

We used our familiar operations: add, subtract, multiply, divide, raise to an exponent, take a root, open brackets, factor etc, to maintain equality while putting the value r on its own on the left hand side.

Your turn!

The circumference of a circle is given by the formula C=2\pi r. Rearrange to make r the subject.

A straight line has equation 3x-5y+15=0. Rearrange to make y the subject.

A straight line has equation x+y=10. Rearrange to make y the subject.

Pythagoras theorem tells us that for a right angled triangle, c^2=a^2+b^2=. Now c^2 is the subject of that formula. Rearrange to make a the subject.

The area of a trapezium is given by the formula A=\Big(\frac{a+b}{2}\Big)h, where a and b are the parallel sides. Rearrange to make a the subject.

 

 

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