Algebra: 3.4 Formulae

1. The following formula calculates the volume,
$V$
, of a sphere, for a given radius,
$r$.
Change the subject of the following formula to calculate the radius.
$$V=\frac{4}{3}\pi {r}^{3}$$

$$r=\sqrt[3]{\frac{3V}{4\pi}}$$

2. The following formula calculates the surface area,
${S}_{A}$,
of a sphere, given you know the radius,
$r$.
Change the subject of the following formula to calculate the radius.
$${S}_{A}=4\pi {r}^{2}$$

$$r=\sqrt{\frac{{S}_{A}}{4\pi}}$$

3. The following formula calculates the surface area,
${S}_{A}$,
of a cone, given you know the radius,
$r$
and the side length,
$S$.
Change the subject of the following formula to calculate the side length.
$${S}_{A}=\pi rS$$

$$S=\frac{{S}_{A}}{\pi r}$$

4. The following formula calculates the area,
$A$,
of a trapezoid, given you know the height,
$h$
and edge lengths,
$a$and
$b$.
Change the subject of the following formula to calculate the height.
$$A=\frac{h}{2}(a+b)$$

$$h=\frac{2A}{(a+b)}$$

## Rearranging

You really need to have got to grips with rearranging formulae to be able to complete these questions.

Remember what you do to one side of the equation you must do the same to the other side.