The moon has a surface area of approximately 14,650,000 mi squared. Estimate its radius to the nearest mile.
Area = 14,650,000 = 4πr^2
Insert value for π and solve for r.
To estimate the radius of the moon, we can make use of the formula for the surface area of a sphere:
Surface Area = 4πr^2
Given that the surface area of the moon is approximately 14,650,000 square miles, we can rearrange the formula to solve for the radius (r):
r = √(Surface Area / (4π))
Now, let's substitute the given values into the formula and calculate the estimated radius:
r = √(14,650,000 / (4π))
r = √(3,690,037.5 / π)
r ≈ √1,174,229.924
r ≈ 1,083.22 miles
Therefore, the estimated radius of the moon to the nearest mile is approximately 1,083 miles.