Question

about 50% of the population of Alaska lives within a 50 mile radius of anchorage. if the total area of Alaska is 586,412 mi.² about what percent of the total land area is within 50 miles of anchorage?

Answer 1

So since it is a 50 mile radius around one point, then it makes a circle.  You need to find the are of the circle to find out how much land that is.  you use the equation A=$\pi$ r².  Plug 50 in for r and you get A= $\pi$ 50². 50²=2500.  Then you multiply that by 3.14 (rounded number of pi) and you get 7850.  So, now you have the total land area, now you need the percent of the total Alaskan land.  To do that, you make a proportion. $\frac{7850}{586,412}$ = $\frac{x}{100}$  Then, you cross multiply and get 785,000=586,412x.  To find out what x is, you divide both sides by 586,412 and get x=1.3386 % .  Hope this helps!!

Answer 2

Percent = portion/total = area/total area
radius means it's a circle, so A=pi*r^2 = (3.1415)(50mi)^2  =2500pi
% = 2500pi/586,412 
use a calulator. then take whatever decimal it gives you and multiply by 100%
say the answer is .12984
.12984 * 100% = 12.984%