\begin{tabular}{l}2.2 .1 Calculate the radius of the centre circle (round off to 2 decimal places) \ 2.2 .2 Calculate the circumference of the centre circle \ 2.2 .3 Calculate the length of lines to be painted if all the lines need to be painted \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

**Step 1. Calculate the radius of the centre circle**

In association football the dimensions of the pitch and its markings are standardised. One of the standard markings is the centre circle whose radius is fixed at  
$$
r = 9.15\text{ m}
$$
(when expressed to 2 decimal places).

---

**Step 2. Calculate the circumference of the centre circle**

The formula for the circumference of a circle is  
$$
C = 2\pi r.
$$
Substitute $$ r = 9.15\text{ m} $$ into the formula:
$$
C = 2\pi (9.15) \approx 2 \times 3.1416 \times 9.15 \approx 57.46\text{ m}.
$$
Thus, the circumference of the centre circle is approximately  
$$
57.46\text{ m}.
$$

---

**Step 3. Calculate the total length of lines to be painted**

A standard football pitch (using one common set of dimensions) has the following painted lines:
- **Perimeter (touch-lines and goal-lines):** For a pitch of length $$105\text{ m}$$ and width $$68\text{ m}$$ the perimeter is  
  $$
  \text{Perimeter} = 2(105 + 68) = 2(173) = 346\text{ m}.
  $$
- **Centre line:** This line divides the pitch into two halves along the length of the pitch, so its length is  
  $$
  105\text{ m}.
  $$
- **Centre circle circumference:** As computed above,  
  $$
  57.46\text{ m}.
  $$

Now, adding these components together gives the total length of the painted lines:
$$
\text{Total length} = 346 + 105 + 57.46 = 508.46\text{ m}.
$$

Rounding to 2 decimal places (if necessary) the total length is  
$$
508.46\text{ m}.
$$

---

**Summary of Answers**

- **2.2.1 Centre circle radius:** $$9.15\text{ m}$$
- **2.2.2 Centre circle circumference:** $$57.46\text{ m}$$
- **2.2.3 Total length of painted lines:** $$508.46\text{ m}$$

*Note:* The calculation in Step 3 is based on one typical set of pitch dimensions (105 m × 68 m) and the standard centre circle radius. In some cases, pitch dimensions might vary; adjust the arithmetic accordingly.
- **2.2.1** The radius of the centre circle is **9.15 meters**. - **2.2.2** The circumference of the centre circle is **57.46 meters**. - **2.2.3** The total length of lines to be painted is **508.46 meters**.

\begin{tabular}{l}2.2 .1 Calculate the radius of the centre circle (round off to 2 decimal places) \\ 2.2 .2 Calculate the circumference of the centre circle \\ 2.2 .3 Calculate the length of lines to be painted if all the lines need to be painted \\ \hline\end{tabular}

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