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.

Hans007
Feb 9, 2018

#1**+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 * 18^{2})m^{2} + 2(1/4)(pi * 8^{2})m^{2}

grazing area = (3/4)(324pi)m^{2} + 2(1/4)(64pi)m^{2}

grazing area = 243pi m^{2} + 32pi m^{2}

grazing area = 275pi m^{2}

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

hectictar
Feb 10, 2018

#1**+2 **

Best Answer

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 * 18^{2})m^{2} + 2(1/4)(pi * 8^{2})m^{2}

grazing area = (3/4)(324pi)m^{2} + 2(1/4)(64pi)m^{2}

grazing area = 243pi m^{2} + 32pi m^{2}

grazing area = 275pi m^{2}

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

hectictar
Feb 10, 2018