riley94
contestada

A dog is attached to a 49 foot rope fastened to the outside corner of a fenced-in garden that measures 42 feet by 51 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander.

Respuesta :

CastleRook
Assuming that the corner of the fence has right angle, the the area that the dog wandered will be given by:
A=θ/360πr²
Where:
θ=360-90=270°
r=49 ft
hence the area will be:
A=270/360×π×49²
A=5657.23 ft²
Thus the dog will wander in the area of 5657.23 ft²

Answer:

5698 sq. cm is the answer.

Step-by-step explanation:

Since dog cannot enter the garden therefore and it can wander as maximum as its rope can move which actually makes a circle. therefore it makes 3rd fourth of circle  with radius 49 cm and then one fourth part  circle with radius 7 cm  with another corner ( From the corner 42 foot away from where the leash begins ,the dog has only 49 - 42 = 7 foot of leash left )

So total area covered by dog = [tex]\frac{3}{4} \pi {(49)}^2[/tex] +

                                                     [tex]\frac{1}{4} \pi {(7)}^2[/tex]

                                                 = [tex]\frac{49}{4} \pi [49(3) + 1][/tex]

                                                  =  [tex]\frac{49}{4} \pi (148)[/tex]

                                                  = 37  (49) ([tex]\frac{22}{7}[/tex]

                                                   = 37x7x22

                                                   =5698  sq cm

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