+50 A fence encloses a square field whose sides measure 8 m. A horse is tethered to 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 13 m long, find the total grazing area of the horse in square metres.
+50 A lot lol... just got a new exam review and need someone to explain the solutions to me.
+129852 We have two areas to consider
(1) The horse will be able to graze a larger area which is the area of a (3/4) circle with a radius of 13
So this area = (3/4) pi *13^2 = (1/4)pi * 3* 13^2
(2) We have two smaller areas that are both quarter-circles with radii of (13 - 8) = 5
So this area = 2 (1/4) *pi * 5^2 = (1/4) pi * 2 * 5^2
So.....the total area =
(1/4) pi [ 3 * 13^2 + 2 * 5^2 ] =
(pi/4) [ 507 + 50 ] =
(pi/4) [ 557] =
(557/4) pi m^2 ≈ 437.5 m^2
