2006 AMC 10A Question 12 - thichhoctoan.com

Question 12

Rolly wishes to secure his dog with an $8$-foot rope to a square shed that is $16$ feet on each side. His preliminary drawings are shown.

Question illustration

Which of these arrangements gives the dog the greater area to roam, and by how many square feet?

$\mathrm{I},$ by $8\pi$
$\mathrm{I},$ by $6\pi$
$\mathrm{II},$ by $4\pi$
$\mathrm{II},$ by $8\pi$
$\mathrm{II},$ by $10\pi$