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Acrivity 1 There is a path of \( I \) me widh arenand the thack. 1.1 Calculate the circumference of one scmi-circle of the track. 1.2 Caleulate the perimeter of the total track. \( \mathrm{I} m \) in width. Caleulate the 1.3 There is a path around the track, w. area of the path. 1.4 The athletics club manager wants to ercet a fence one metre from the track (on the outside perimeter of the path). Calculate how many metres of fencing he will have to buy. 1.5 The fence must be supported by poles planted three metres apart. How many poles are needed? If he pays R115,95 per running metre of fencing, what is the cost of

Ask by George Schneider. in South Africa
Mar 10,2025

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To calculate the required measurements and costs for the athletics track and fencing: 1. **Circumference of One Semicircle**: \[ C_{\text{semicircle}} = \pi r \] (Where \( r \) is the radius of the semicircle.) 2. **Perimeter of the Total Track**: \[ P = 2 \cdot C_{\text{semicircle}} + 2L \] (Where \( L \) is the length of the straight sections.) 3. **Area of the Path**: \[ A = \text{Area of larger rectangle} - \text{Area of smaller rectangle} \] 4. **Fencing Requirement**: - New perimeter = Outer perimeter of the path. - Total fencing needed = New perimeter. 5. **Number of Poles Needed**: \[ \text{Number of poles} = \frac{\text{Total fencing}}{3} \text{ meters apart} \] 6. **Cost of Fencing**: \[ \text{Cost} = \text{Total fencing} \times R115.95 \] **Note**: The value of \( I \) (width of the path) is required to perform the calculations accurately.

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Bonus Knowledge

To find the circumference of one semicircle, you use the formula \( C = \pi r \), where \( r \) is the radius. If the radius of the semicircle is half the width of the circle at its widest point, you can substitute the value into the formula. Remember that since it's a semicircle, you'll need to divide the full circle's circumference by 2, giving you an engaging way to think about geometry! For a complete solution, you'll also need to calculate the area of the path surrounding the track. This can be found by determining the area difference between two circles: one representing the inner track and another the outer path. Subtract the area of the inner circle from that of the outer circle, and you'll find the area of the path—perfect for visualizing math in a real-world context, like creating sunbathing spaces around a pool!

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