\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**.

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

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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