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A dog's leash is 4 m long and is attached to the corner of a 2 m × 2 m square doghouse at C, as shown. The dog is attached to the other end of the leash, at D. What is the area outside of the doghouse in which the dog can play? (A) 14π m^2 (B) 16π m^2 (C) 20π m^2 (D) 15π m^2 (E) 24π m^2

Respuesta :

MrRoyal

Answer:

[tex]Area = 16\pi[/tex]

Step-by-step explanation:

Given

[tex]l =4m[/tex] -- length of leash

Required

The area which the dog can play

The dog can play in a circular path and the radius of the path is the length of the leash.

So, the area is:

[tex]Area = \pi r^2[/tex]

Where:

[tex]l = r=4[/tex]

So, we have

[tex]Area = \pi * 4^2[/tex]

[tex]Area = \pi * 16[/tex]

[tex]Area = 16\pi[/tex]

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