Thread: Surface Area

Many countries extend their borders by making a claim over territorial waters inside a defined km distance from their coastline.
What is the size (radius and area) of a circular island claiming a territorial waters of limit of 40km whose landmass is 75% of all territories claimed? Describe your method of finding a solution.

Could someone please show me the working out?










Answer: r=259km, area=210 026km^2
Thanks

Originally Posted by Fibonacci

Many countries extend their borders by making a claim over territorial waters inside a defined km distance from their coastline.
What is the size (radius and area) of a circular island claiming a territorial waters of limit of 40km whose landmass is 75% of all territories claimed? Describe your method of finding a solution.

Could someone please show me the working out?

Answer: r=259km, area=210 026km^2
Thanks

Hello,

let r be the radius of the island, then
(r+40) is the radius of the complete territory:
75% = (3/4) (for affirmation only )

(3/4) * π * (r+40)² = π * r²

Expand the LHS and collect all terms on the LHS. You'll get:

-(1/4)πr² + 60πr + 1200 = 0 . Divide by -(1/4)π

r² - 240r - 4800 = 0.

r ≈ 258.564 or r ≈ -18.564 The negative solution doesn't make much sense here.

Area of the island: A(r) = π * r² that means: A(258.564) ≈ 210,032 km²