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A dog is tied to the corner of a fence with a 9 foot chain. If the angle of that corner of the fence is 120 degrees, how many square feet does the dog have to walk around (the dog is tied inside, not outside, the fence)?
(A) 19π
(B) 27
(C) 27π
(D) 81
(E) 81π
(A) 19π
(B) 27
(C) 27π
(D) 81
(E) 81π
07 Mar 2022, 08:44
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The fence is 120 degrees, since the dog is on the outside of the fence, he is in a sector that is 360-120 = 240 degrees.
Now to get area the dog has to walk around in we need to find the area he is able to walk with with a radius of 9 (his chain) and multiply that by the section available to him that isn't covered by a wall 240/360 or 2/3.
Area = 9^2 π * 2/3 = 27π
==> C
Now to get area the dog has to walk around in we need to find the area he is able to walk with with a radius of 9 (his chain) and multiply that by the section available to him that isn't covered by a wall 240/360 or 2/3.
Area = 9^2 π * 2/3 = 27π
==> C
01 May 2022, 12:08
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Charli08
The fence is 120 degrees, since the dog is on the outside of the fence, he is in a sector that is 360-120 = 240 degrees.
Now to get area the dog has to walk around in we need to find the area he is able to walk with with a radius of 9 (his chain) and multiply that by the section available to him that isn't covered by a wall 240/360 or 2/3.
Area = 9^2 π * 2/3 = 27π
==> C
Now to get area the dog has to walk around in we need to find the area he is able to walk with with a radius of 9 (his chain) and multiply that by the section available to him that isn't covered by a wall 240/360 or 2/3.
Area = 9^2 π * 2/3 = 27π
==> C
Hi!
Could you please explain how you got that result. I did the math and got a different one. Thanks!
9^2 π * 2/3 = 81π * 2/3 = 54π
