Question

what is the area of a circle that has a radius of 12 cm. use \\(\pi = 3.14\\) and round to the nearest \\(\text{cm}^2\\). select one: a. the area of the circle is 75 \\(\text{cm}^2\\). b. the area of the circle is 118 \\(\text{cm}^2\\). c. the area of the circle is 779 \\(\text{cm}^2\\). d. the area of the circle is 1810 \\(\text{cm}^2\\). e. the area of the circle is 452 \\(\text{cm}^2\\). wilma measured the radius of a circle and (correctly) got a length of 46 cm. if pebbles used this information to determine the area of a circle, she will get an area of ?

Explanation:

Step1: Recall circle area formula

The area of a circle is given by $A = \pi r^2$, where $r$ is the radius, and $\pi=3.14$.

Step2: Substitute $r=12$ into formula

$$A = 3.14 \times 12^2$$

Step3: Calculate $12^2$ first

$12^2 = 144$

Step4: Compute final area

$$A = 3.14 \times 144 = 452.16$$

Step5: Round to nearest whole number

$452.16 \approx 452$

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Step1: Find radius from circumference

Wilma's measurement is the circumference: $C=46$ cm. The formula for circumference is $C=2\pi r$. Solve for $r$:
$$r = \frac{C}{2\pi} = \frac{46}{2 \times 3.14} \approx \frac{46}{6.28} \approx 7.325$$

Step2: Calculate area with this radius

$$A = \pi r^2 = 3.14 \times (7.325)^2$$

Step3: Compute $r^2$

$(7.325)^2 \approx 53.6556$

Step4: Find final area

$$A \approx 3.14 \times 53.6556 \approx 168.48$$

Step5: Round to nearest whole number

$168.48 \approx 168$ cm²

Answer:

For the first question (radius = 12 cm):
e. The area of the circle is 452 cm².

For Pebbles' calculation (circumference = 46 cm):
168 cm²