Question

1. find the area of the circle. find the solution in terms of \\(\pi\\), and then convert the result into decimal form rounded to the nearest hundredth using 3.14 for \\(\pi\\).

the circumference is \\(0.6\pi\\) miles.
\\(\square\\) \\(a = 1.2\pi\\ \text{mi}^2\\)
\\(\square\\) \\(a = 0.36\pi\\ \text{mi}^2\\)
\\(\square\\) \\(a = 3.77\\ \text{mi}^2\\)
\\(\square\\) \\(a = 0.09\pi\\ \text{mi}^2\\)
\\(\square\\) \\(a = 1.13\\ \text{mi}^2\\)
\\(\square\\) \\(a = 0.28\\ \text{mi}^2\\)

Explanation:

Step1: Solve for radius from circumference

Circumference formula: $C = 2\pi r$. Given $C=0.6\pi$,
$$0.6\pi = 2\pi r$$
$$r = \frac{0.6\pi}{2\pi} = 0.3 \text{ mi}$$

Step2: Calculate area in terms of $\pi$

Area formula: $A = \pi r^2$. Substitute $r=0.3$,
$$A = \pi (0.3)^2 = 0.09\pi \text{ mi}^2$$

Step3: Convert to decimal form

Use $\pi=3.14$,
$$A = 0.09 \times 3.14 = 0.2826 \approx 0.28 \text{ mi}^2$$

Answer:

$A = 0.09\pi \text{ mi}^2$, $A = 0.28 \text{ mi}^2$
(The correct options are $\boldsymbol{\square\ A = 0.09\pi\ \text{mi}^2}$ and $\boldsymbol{\square\ A = 0.28\ \text{mi}^2}$)