Question
If the distance halfway around Mercury is 4,761 mi., then what is the length of the diameter of the planet to the nearest mile?(1 point)
Responses
1,515 mi.
1,515 mi.
14,957 mi.
14,957 mi.
4,761 mi.
4,761 mi.
3,031 mi.
Responses
1,515 mi.
1,515 mi.
14,957 mi.
14,957 mi.
4,761 mi.
4,761 mi.
3,031 mi.
Answers
Answered by
GPT-4o mini
To find the diameter of Mercury based on the distance halfway around the planet (which is the circumference divided by 2), we first note that the given distance halfway around Mercury is 4,761 miles. This means that the full circumference \( C \) is:
\[ C = 2 \times 4,761 \text{ mi} = 9,522 \text{ mi} \]
The formula for the circumference of a circle is:
\[ C = \pi \times d \]
where \( d \) is the diameter. We can rearrange this formula to solve for the diameter:
\[ d = \frac{C}{\pi} \]
Substituting the calculated circumference:
\[ d = \frac{9,522 \text{ mi}}{\pi} \]
Using \( \pi \approx 3.14159 \):
\[ d \approx \frac{9,522 \text{ mi}}{3.14159} \approx 3,032 \text{ mi} \]
Rounding to the nearest mile, we find:
**Diameter of Mercury \( \approx 3,031 \text{ mi}**.
The correct response is:
**3,031 mi.**
\[ C = 2 \times 4,761 \text{ mi} = 9,522 \text{ mi} \]
The formula for the circumference of a circle is:
\[ C = \pi \times d \]
where \( d \) is the diameter. We can rearrange this formula to solve for the diameter:
\[ d = \frac{C}{\pi} \]
Substituting the calculated circumference:
\[ d = \frac{9,522 \text{ mi}}{\pi} \]
Using \( \pi \approx 3.14159 \):
\[ d \approx \frac{9,522 \text{ mi}}{3.14159} \approx 3,032 \text{ mi} \]
Rounding to the nearest mile, we find:
**Diameter of Mercury \( \approx 3,031 \text{ mi}**.
The correct response is:
**3,031 mi.**
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