Find the radii of circles with the following areas: \( \begin{array}{ll}154 \mathrm{~cm}^{2} & \text { b } 1386 \mathrm{~cm}^{2} \\ 86 \frac{5}{8} \mathrm{~m}^{2} & \text { d } 6.16 \mathrm{ha}\end{array} \)

To find the radii of circles given their areas, we can use the formula for the area of a circle: \[ A = \pi r^2 \] We can rearrange this formula to solve for the radius \( r \): \[ r = \sqrt{\frac{A}{\pi}} \] Let's calculate the radii for each area provided: 1. **For 154 cm²:** \[ r = \sqrt{\frac{154}{\pi}} \approx \sqrt{\frac{154}{3.14}} \approx \sqrt{49} \approx 7 \text{ cm} \] 2. **For 1386 cm²:** \[ r = \sqrt{\frac{1386}{\pi}} \approx \sqrt{\frac{1386}{3.14}} \approx \sqrt{442} \approx 21.0 \text{ cm} \] 3. **For 86 \(\frac{5}{8}\) m²:** First, convert \(86 \frac{5}{8}\) to an improper fraction: \[ 86 \frac{5}{8} = \frac{693}{8} \text{ m²} \] Find the radius: \[ r = \sqrt{\frac{\frac{693}{8}}{\pi}} \approx \sqrt{\frac{693}{8 \times 3.14}} \approx \sqrt{\frac{693}{25.12}} \approx \sqrt{27.55} \approx 5.25 \text{ m} \] 4. **For 6.16 ha:** First, convert hectares to square meters: \[ 6.16 \text{ ha} = 6.16 \times 10^4 \text{ m²} = 61600 \text{ m²} \] Find the radius: \[ r = \sqrt{\frac{61600}{\pi}} \approx \sqrt{\frac{61600}{3.14}} \approx \sqrt{19658.6} \approx 140 \text{ m} \] To summarize the calculated radii for each area: - a) \( 7 \text{ cm} \) - b) \( 21.0 \text{ cm} \) - c) \( 5.25 \text{ m} \) - d) \( 140 \text{ m} \)