Multiples of pi

#### Tier: #Foundation #Higher

Description

Many circle calculations produce answers as multiples of $\pi$ (e.g. $6\pi$, $\frac{25\pi}{4}$). Leaving answers in terms of $\pi$ gives an exact value.

When to leave in terms of $\pi$: questions will say "leave your answer in terms of $\pi$" or "give an exact answer".

Examples: $$\text{Circumference} = 2\pi r = 2\pi \times 5 = 10\pi \text{ cm}$$ $$\text{Area} = \pi r^2 = \pi \times 4^2 = 16\pi \text{ cm}^2$$

Simplifying multiples of $\pi$: $$3\pi + 5\pi = 8\pi$$ $$\frac{1}{2} \times \pi \times 6^2 = 18\pi$$

Do not evaluate $\pi$ numerically (3.14159…) if an exact answer is required.

Sector area: $\frac{\theta}{360} \times \pi r^2$ — keep in terms of $\pi$ until the final step if needed.

Common error: pressing = on the calculator and writing a rounded decimal when an exact answer is required.

Links

Substitution Area of a circle Arcs & sectors