Question 222747
It has been estimated that 900 curies of a radioactive substance introduced at
 a point on the surface of the open sea would spread over an area of 24000km^2 in 30 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.
:
Do not simplify the number under the radical.
:
I think what you got is pretty close, here's my take on this
:
Find the value of r when t = 30 days and area = 24000
:
{{{pi*(30r)^2 = 24000}}}
:
{{{pi*900*r^2 = 24000}}}
:
{{{r^2 = 24000/(900*pi)}}}
Reduce the fraction
{{{r^2 = 80/(3*pi)}}}
:
{{{r = sqrt(80/(3pi))}}}
:
:
r as a function of t
{{{r = sqrt(80/(3pi))*t}}}
:
:
Check this find radius when t = 30 days
{{{r = sqrt(80/(3pi))*30}}}
r = 87.4 km
:
Find the area using this value for r
A = pi*87.4^2  = 24,000 sq/km; confirms our solution