1. **Problem Statement:** Calculate the radius $x$ for sectors with given areas and central angles (Question 4). 2. **Formula:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by: $$A = \frac{\theta}{360} \pi r^2$$ 3. **Step-by-step solutions:** **(a) Given:** $A=20$ cm², $\theta=115^\circ$, find $x$. $$20 = \frac{115}{360} \pi x^2$$ Multiply both sides by $\frac{360}{115 \pi}$: $$x^2 = 20 \times \frac{360}{115 \pi}$$ Simplify: $$x^2 = \frac{7200}{115 \pi}$$ Calculate $x$: $$x = \sqrt{\frac{7200}{115 \pi}}$$ Numerical approximation: $$x \approx \sqrt{\frac{7200}{361.283}} \approx \sqrt{19.93} \approx 4.46 \text{ cm}$$ **(b) Given:** $A=98$ cm², $\theta=26^\circ$, find $x$. $$98 = \frac{26}{360} \pi x^2$$ Multiply both sides by $\frac{360}{26 \pi}$: $$x^2 = 98 \times \frac{360}{26 \pi}$$ Simplify: $$x^2 = \frac{35280}{26 \pi}$$ Calculate $x$: $$x = \sqrt{\frac{35280}{26 \pi}}$$ Numerical approximation: $$x \approx \sqrt{\frac{35280}{81.681}} \approx \sqrt{431.9} \approx 20.78 \text{ cm}$$ **(c) Given:** $A=1$ m², $\theta=252^\circ$, find $x$. $$1 = \frac{252}{360} \pi x^2$$ Multiply both sides by $\frac{360}{252 \pi}$: $$x^2 = 1 \times \frac{360}{252 \pi}$$ Simplify: $$x^2 = \frac{360}{252 \pi}$$ Calculate $x$: $$x = \sqrt{\frac{360}{252 \pi}}$$ Numerical approximation: $$x \approx \sqrt{\frac{360}{791.681}} \approx \sqrt{0.4547} \approx 0.674 \text{ m}$$