Rearranging Formulae Practice Questions

The total surface area $A$ of a closed cylinder of radius $r$ and height $h$ is given by

$$A = 2\pi r h + 2\pi r^{2}$$

Make $h$ the subject of the formula.

The volume $V$ of a sphere of radius $r$ is given by

$$V = \frac{4}{3}\pi r^{3}$$

Make $r$ the subject of the formula.

The time $T$ for one complete swing of a pendulum of length $L$ is given by

$$T = 2\pi\sqrt{\frac{L}{g}}$$

Make $g$ the subject of the formula.

Rearrange $3(p - 2q) = q(p + 5)$ to make $p$ the subject.

Rearrange $y = \dfrac{\sqrt{x} + 1}{\sqrt{x} - 3}$ to make $x$ the subject.

Make $T$ the subject of the formula.

Make $b$ the subject of the formula.

Show that $h = \dfrac{96 - x^{2}}{4x}$

Two formulae are given below.

$$p = \frac{2q^{2}}{5} \qquad \qquad q = \frac{3}{r + 1}$$

Express $r$ in terms of $p$.