EXERCISE 3 1. Consider the diagram on the right. a) Find the values of \( p \) and \( q \) (leave your answers in surd form) and then calculate \( x \) (correct to 2 decimal places). b) Round off \( p \) and \( q \) (to 2 decimal places) and then calculate \( x \) (correct to 2 decimal places). c) Compare the values of \( x \) you got in 1.a) and \( 1 . \mathrm{b} \) ) and comment brlefly on the accuracy of your answers. 2. The area of a circle is given by \( A=\pi r^{2} \) and the circumference is given by \( C=2 \pi r \). If \( C=500 \) m, calculate: a) \( r \) (correct to 2 decimal places) and use this value to calculate \( A \) (corrcct to 2 decimal places). b) \( r \) but do not round off your answer before you calculate \( A \). c) Compare the values of \( A \) you got in 2 (a) and \( 2(b) \) and comment briefly on the accuracy of your answers. \( \begin{array}{l}\text { REMEMBER } \\ \text { Only your founded off, not the } \\ \text { calculations you do along the } \\ \text { way. }\end{array} \)

Sure, let's tackle **Exercise 3** step by step. Since part **1** refers to a diagram that isn't provided, we'll focus on **part 2**, which is fully described. If you can provide details or descriptions of the diagram for part 1, I'd be happy to assist with that as well. --- ### **2. Calculating Radius and Area of a Circle** Given: - **Circumference (C)** = 500 meters - **Formulas:** - Area, \( A = \pi r^{2} \) - Circumference, \( C = 2\pi r \) #### **a) Find \( r \) (rounded to 2 decimal places) and then calculate \( A \) (rounded to 2 decimal places).** 1. **Calculate the Radius (\( r \)):** \[ C = 2\pi r \implies r = \frac{C}{2\pi} = \frac{500}{2\pi} = \frac{250}{\pi} \] \[ r \approx \frac{250}{3.141592653589793} \approx 79.5775\, \text{meters} \] **Rounded to 2 decimal places:** \[ r \approx 79.58\, \text{meters} \] 2. **Calculate the Area (\( A \)):** \[ A = \pi r^{2} = \pi \times (79.58)^{2} \approx \pi \times 6333.3764 \approx 19903.535\, \text{m}^{2} \] **Rounded to 2 decimal places:** \[ A \approx 19903.54\, \text{m}^{2} \] #### **b) Find \( r \) without rounding off before calculating \( A \).** 1. **Calculate the Radius (\( r \)) Without Rounding:** \[ r = \frac{250}{\pi} \approx 79.57747154594767\, \text{meters} \] 2. **Calculate the Area (\( A \)) Using the Unrounded \( r \):** \[ A = \pi r^{2} = \pi \times \left(\frac{250}{\pi}\right)^{2} = \pi \times \frac{62500}{\pi^{2}} = \frac{62500}{\pi} \approx 19904.77796\, \text{m}^{2} \] **Rounded to 2 decimal places:** \[ A \approx 19904.78\, \text{m}^{2} \] #### **c) Compare the values of \( A \) from parts 2.a and 2.b and comment on the accuracy.** - **Area from part 2.a:** \( 19903.54\, \text{m}^{2} \) - **Area from part 2.b:** \( 19904.78\, \text{m}^{2} \) **Difference:** \[ 19904.78 - 19903.54 = 1.24\, \text{m}^{2} \] **Comment on Accuracy:** The area calculated in **part 2.b** is slightly more accurate than that in **part 2.a**. This is because in part 2.a, the radius was rounded off to two decimal places before calculating the area, introducing a minor rounding error. In contrast, part 2.b uses the exact value of \( r \) until the final step, minimizing rounding errors and yielding a more precise result. --- If you can provide the diagram or additional details for **part 1**, I'd be glad to help you work through it!