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

Question

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

UpStudy AI · Accepted Answer

We use the formula for the area of a circle:

$$
A = \pi r^2
$$

Solving for the radius $$ r $$ gives:

$$
r = \sqrt{\frac{A}{\pi}}
$$

### Part (a): $$ A = 154\,\text{cm}^2 $$

$$
r = \sqrt{\frac{154}{\pi}} \approx \sqrt{\frac{154}{3.14159}} \approx \sqrt{49} = 7\,\text{cm}
$$

### Part (b): $$ A = 1386\,\text{cm}^2 $$

$$
r = \sqrt{\frac{1386}{\pi}} \approx \sqrt{\frac{1386}{3.14159}} \approx \sqrt{441} = 21\,\text{cm}
$$

### Part (c): $$ A = 86\frac{5}{8}\,\text{m}^2 $$

First, convert the mixed number to an improper fraction:

$$
86\frac{5}{8} = \frac{86 \times 8 + 5}{8} = \frac{688 + 5}{8} = \frac{693}{8}\,\text{m}^2
$$

Then, the radius is:

$$
r = \sqrt{\frac{\frac{693}{8}}{\pi}} = \sqrt{\frac{693}{8\pi}} \approx \sqrt{\frac{86.625}{3.14159}} \approx \sqrt{27.576} \approx 5.25\,\text{m}
$$

### Part (d): $$ A = 6.16\,\text{ha} $$

Convert hectares to square meters (since $$1\,\text{ha} = 10\,000\,\text{m}^2$$):

$$
A = 6.16 \times 10\,000 = 61\,600\,\text{m}^2
$$

Now,

$$
r = \sqrt{\frac{61\,600}{\pi}} \approx \sqrt{\frac{61\,600}{3.14159}} \approx \sqrt{19\,616.3} \approx 140\,\text{m}
$$
The radii of the circles are as follows: - **a)** 7 cm - **b)** 21 cm - **c)** Approximately 5.25 meters - **d)** 140 meters

Find the radii of circles with the following areas:

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Part (a):

Part (b):

Part ©:

Part (d):

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