The gravitational force exerted by a planet is inversely proportional to the square of the distance to the center of the planet. Thus, the weight, w, of an object at a distance, r, from a planet's center is given by
k
w = ---, with k constant.
r²

A gravitational force of 2020 pounds will kill a110-pound person. Suppose the earth's radius were to shrink with its mass remaining the same. What is the smallest radius at which the 110-pound person could survive?
Round your answer to three decimal places.