It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 20,000 km2 in 20 days. Assuming that the area covered by the radioactive substance is a linear function of time t and is always circular in shape, express the radius r of the contamination as a function of t.

 

Apparently Area = constant * t.

As 20,000 km2 = constant * 20 days, the constant equals 1,000 km2/day

 

Therefore Area = 1,000 km^2/day * t

On the other hand Area = pi r^2.

So pi r^2 = 1,000 km^2/day * t, meaning that

radius r = sqrt (1000/pi km^2/day) * t^(1/2)

 

I got this far but I don't think the answer has km as part of the solution. I'm sure that there is a pi involved. Any ideas?

Your formula is correct. Why wouldn't the answer have a km? You're finding a length, which is measured in km.

looks like you got it right. Why wouldn't a radius have a unit of distance in it?

We have to enter our answers online and it says I've gotten the wrong answer. . . How do I enter the answer in? I'm very confused becuase I feel like I've done it right. . .

i have no idea how you are supposed to submit it. why not send an email to the person running thequiz and ask them about answer format.