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# A fence encloses

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A fence encloses a square field whose sides measure 10m. A horse is tethered on a rope that is attached to a corner post of the field so that the horse is outside the fence.If the rope holding the horse is 18m long, find the total grazing area of the horse in square metres.

Feb 9, 2018

#1
+8146
+2

When the horse gets to a corner of the fence that is adjacent to the corner where the rope is attached, he will have  8m  of rope left. So there are two quarters of a circle with a radius of  8m in the grazing area. And there are three quarters of a circle with a radius of 18m in the grazing area.

grazing area   =   (3/4)(pi * 182)m2   +   2(1/4)(pi * 82)m2

grazing area   =   (3/4)(324pi)m2   +   2(1/4)(64pi)m2

grazing area   =   243pi m2   +   32pi m2

grazing area   =   275pi m2

Here is a link to a picture because it didn't show up well in the post:

https://i.imgur.com/FocSpyx.png

Feb 10, 2018

#1
+8146
+2

When the horse gets to a corner of the fence that is adjacent to the corner where the rope is attached, he will have  8m  of rope left. So there are two quarters of a circle with a radius of  8m in the grazing area. And there are three quarters of a circle with a radius of 18m in the grazing area.

grazing area   =   (3/4)(pi * 182)m2   +   2(1/4)(pi * 82)m2

grazing area   =   (3/4)(324pi)m2   +   2(1/4)(64pi)m2

grazing area   =   243pi m2   +   32pi m2

grazing area   =   275pi m2

Here is a link to a picture because it didn't show up well in the post:

https://i.imgur.com/FocSpyx.png

hectictar Feb 10, 2018