Question

eugene knows the circumference of a circle is 125.6 meters. does he have enough information to find the area?

yes, because he could divide by 3.14 to find the diameter and then divide that result by 2 to find the radius. once he has the radius, he can use the formula.
yes, because the area will just be twice the circumference so all he has to do is multiply by 2.
no, because the circumference equals \\(c = \text{diameter} \cdot \pi\\) and there is no \\(\pi\\) in 125.6.
no, because the circumference equals \\(c = \text{diameter} \cdot \pi\\) so he could only find the diameter. he needs the radius for the area formula.

Explanation:

Relate circumference to radius

Using the Circumference of a Circle knowledge point

$$
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$$

Calculate area from radius

Using the Area of a Circle knowledge point

$$
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$$

Evaluate the given options

Using the Circumference of a Circle and Area of a Circle knowledge points

$$ \text{Option 1 matches the correct logical steps to find the area.} $$

Answer:

• (A) Yes, because he could divide by 3.14 to find the diameter and then divide that result by 2 to find the radius. Once he has the radius, he can use the formula. (Correct answer)
• (B) Yes, because the area will just be twice the circumference so all he has to do is multiply by 2.
• (C) No, because the circumference equals \(C = (\text{Diameter}) \cdot \pi\) and there is no \(\pi\) in 125.6.
• (D) No, because the circumference equals \(C = (\text{Diameter}) \cdot \pi\) so he could only find the diameter. He needs the radius for the area formula.