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)

• 14,957 mi.
• 1,515 mi.
• 3,031 mi.
• 4,761 mi.

1 answer

To find the diameter of Mercury based on the distance halfway around the planet (which is the circumference divided by 2), we can use the relationship between the circumference and diameter of a circle, which is given by the formula:

\[ C = \pi \times d \]

where \(C\) is the circumference and \(d\) is the diameter. Since we have the distance halfway around Mercury (4,761 miles), we can first calculate the full circumference by multiplying this distance by 2:

\[ C = 2 \times 4,761 \text{ mi} = 9,522 \text{ mi} \]

Now, we can rearrange the circumference formula to find the diameter:

\[ d = \frac{C}{\pi} \]

Substituting the value we found for \(C\):

\[ d = \frac{9,522 \text{ mi}}{\pi} \approx \frac{9,522 \text{ mi}}{3.14159} \approx 3,031 \text{ mi} \]

Thus, the length of the diameter of Mercury, to the nearest mile, is approximately:

3,031 mi.