Question

A dog is chained on a $6ft$ leash, fastened to the corner of a rectangular building. Calculate, about how much area does the dog have to move in.

• A. $27f{t}^2$
• B. $36f{t}^2$
• C. $56.55f{t}^2$
• D. $84.82f{t}^2$

Answer 1

The correct option is D $84.82f{t}^2$

A dog is chained on a $6$ ft leash to the corner of a rectangular building.
Since the building is rectangular, the dog is left with an angle of $360-90={270}^o$ for it to roam around.
Also, the length of the leash will act as the radius of this sector.
$\therefore$ Area of the sector $=\frac{270}{360}\times \pi \times 6^2$
$=\frac{3}{4}\times \pi \times 36$
$=84.82f{t}^2$